Dic₉₄₀₁ #49178202

order	37604
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₉₄₀₁
unambiguous semidirect product	C₇⋊Dic₁₃₄₃
unambiguous semidirect product	C₇₉⋊Dic₁₁₉

Splittings

derived, Hall	C₇×C₁₇×C₇₉ ⋊ C₄
Hall	C₁₇×C₇₉ ⋊ Dic₇
Hall	C₇×C₇₉ ⋊ Dic₁₇
Hall	C₇×C₁₇ ⋊ Dic₇₉
Sylow	C₇₉ ⋊ Dic₁₁₉
Sylow	C₁₇ ⋊ Dic₅₅₃
Sylow	C₇ ⋊ Dic₁₃₄₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₉₄₀₁
commutator, hypocenter	C₇×C₁₇×C₇₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₇×C₁₇×C₇₉	C₂
LCS	G ▷ C₇×C₁₇×C₇₉
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 107
transitive degree	μ_t(G) = 37604

A minimal faithful permutation representation — 2 generators on 107 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);(1,3,2,4)(6,11)(7,10)(8,9)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(30,107)(31,106)(32,105)(33,104)(34,103)(35,102)(36,101)(37,100)(38,99)(39,98)(40,97)(41,96)(42,95)(43,94)(44,93)(45,92)(46,91)(47,90)(48,89)(49,88)(50,87)(51,86)(52,85)(53,84)(54,83)(55,82)(56,81)(57,80)(58,79)(59,78)(60,77)(61,76)(62,75)(63,74)(64,73)(65,72)(66,71)(67,70)(68,69)

Polycyclic presentation:

2,7,17,79,2|a^2=e,b^a=b^6,c^a=c^16,d^a=d^78

Conjugacy classes & character table

9404 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37604, 8);

Dic9401 #49178202