Dic₈₃₉₅ #46777153

order	33580
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₈₃₉₅
unambiguous semidirect product	C₂₃⋊Dic₃₆₅

Splittings

derived, Hall	C₅×C₂₃×C₇₃ ⋊ C₄
Hall	C₂₃×C₇₃ ⋊ Dic₅
Hall	C₅×C₇₃ ⋊ Dic₂₃
Hall	C₅×C₂₃ ⋊ Dic₇₃
Sylow	C₇₃ ⋊ Dic₁₁₅
Sylow	C₂₃ ⋊ Dic₃₆₅
Sylow	C₅ ⋊ Dic₁₆₇₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₃₉₅
commutator, hypocenter	C₅×C₂₃×C₇₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₂₃×C₇₃	C₂
LCS	G ▷ C₅×C₂₃×C₇₃
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 105
transitive degree	μ_t(G) = 33580

A minimal faithful permutation representation — 2 generators on 105 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);(1,3,2,4)(6,9)(7,8)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(34,105)(35,104)(36,103)(37,102)(38,101)(39,100)(40,99)(41,98)(42,97)(43,96)(44,95)(45,94)(46,93)(47,92)(48,91)(49,90)(50,89)(51,88)(52,87)(53,86)(54,85)(55,84)(56,83)(57,82)(58,81)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71)(69,70)

Polycyclic presentation:

2,5,23,73,2|a^2=e,b^a=b^4,c^a=c^22,d^a=d^72

Conjugacy classes & character table

8398 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33580, 8);

Dic8395 #46777153