Dic₉₃₈₇ #49176290

order	37548
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₉₃₈₇
unambiguous semidirect product	C₇⋊Dic₁₃₄₁
unambiguous semidirect product	C₉⋊Dic₁₀₄₃

Splittings

derived, Hall	C₇×C₉×C₁₄₉ ⋊ C₄
Hall	C₉×C₁₄₉ ⋊ Dic₇
Hall	C₇×C₁₄₉ ⋊ Dic₉
Sylow	C₁₄₉ ⋊ Dic₆₃
Hall	C₇×C₉ ⋊ Dic₁₄₉
Sylow	C₉ ⋊ Dic₁₀₄₃
Sylow	C₇ ⋊ Dic₁₃₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₃₈₇
commutator, hypocenter	C₇×C₉×C₁₄₉	C₄
Frattini	C₂×C₃	D₃₁₂₉
Fitting, cosocle	C₂×C₇×C₉×C₁₄₉	C₂
socle, prime radical	C₂×C₃×C₇×C₁₄₉	D₃
LCS	G ▷ C₇×C₉×C₁₄₉
UCS	C₁ ◁ C₂

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 169
transitive degree	μ_t(G) = 37548

A minimal faithful permutation representation — 2 generators on 169 points:

(1,2)(3,4)(5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,20)(16,19)(17,18)(22,169)(23,168)(24,167)(25,166)(26,165)(27,164)(28,163)(29,162)(30,161)(31,160)(32,159)(33,158)(34,157)(35,156)(36,155)(37,154)(38,153)(39,152)(40,151)(41,150)(42,149)(43,148)(44,147)(45,146)(46,145)(47,144)(48,143)(49,142)(50,141)(51,140)(52,139)(53,138)(54,137)(55,136)(56,135)(57,134)(58,133)(59,132)(60,131)(61,130)(62,129)(63,128)(64,127)(65,126)(66,125)(67,124)(68,123)(69,122)(70,121)(71,120)(72,119)(73,118)(74,117)(75,116)(76,115)(77,114)(78,113)(79,112)(80,111)(81,110)(82,109)(83,108)(84,107)(85,106)(86,105)(87,104)(88,103)(89,102)(90,101)(91,100)(92,99)(93,98)(94,97)(95,96)

Polycyclic presentation:

2,3,7,149,2,3|a^2=e,b^3=f^2,b^a=b^2f,c^a=c^6,d^a=d^148,f^a=f^2

Conjugacy classes & character table

9390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37548, 9);

Dic9387 #49176290