#27123141

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹³

Aliases

No aliases for this group.

Splittings

Fitting	C₂×C₄×#41×C₄₇ ⋊ C₂
Sylow	C₄₇ ⋊ #62686

Subgroups

	subgroup	G/H
center	C₄²	C₂³×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄×#41×C₄₇	C₂
hypercenter	C₂×C₄×#41	D₄₇
hypocenter	C₄₇	#62686
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₂×C₄×#41

7226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 6 generators on 71 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(48,50,51,54)(49,53,52,55);(56,59,60,66)(57,63,62,69)(58,65,64,70)(61,68,67,71);(57,62)(61,67)(63,69)(68,71);(57,62)(58,64)(63,69)(65,70);(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)(49,52)(53,55)(56,58)(57,61)(59,65)(60,64)(62,67)(63,68)(66,70)(69,71);(48,49)(50,53)(51,52)(54,55)(56,57)(58,61)(59,63)(60,62)(64,67)(65,68)(66,69)(70,71)

Polycyclic presentation:

2^8,47|e^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dh,c^b=ch,i^b=i^46

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1076431);