C₂×(C₃₁⋊C₉)⋊D₃₁ #46829316

order	34596
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×(C₃₁⋊C₉)⋊D₃₁
unambiguous semidirect product	(C₂×C₃₁⋊C₉)⋊D₃₁

Splittings

derived, Sylow	C₃₁² ⋊ C₂²×C₉
Hall	C₃₁×C₃₁⋊C₉ ⋊ C₂²
Hall	C₂×C₃₁⋊D₃₁ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₃₁⋊C₃)⋊D₃₁
commutator, hypocenter	C₃₁²	C₂²×C₉
Frattini	C₃	C₂×(C₃₁⋊C₃)⋊D₃₁
Fitting, socle	C₂×C₃×C₃₁²	C₂×C₃
prime radical	C₂×C₃×C₃₁⋊D₃₁	C₃
cosocle	C₃×C₃₁²	C₂²×C₃
LCS	G ▷ C₃₁²
UCS	C₁ ◁ C₂×C₃

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 558

A minimal faithful permutation representation — 2 generators on 73 points:

(3,7,11,5,10,6,8,4,9)(13,17,18,14,15,19)(16,25,26,20,21,33)(22,36,37,28,29,41)(23,35,31,30,27,24)(32,34,42,38,39,40)(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);(1,2)(12,13,16,22,30,15,19,24,32,39,21,27,33,37,42,29,36,40,41,26,35,25,34,38,31,18,17,23,28,20,14)(43,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45)

Conjugacy classes & character table

1236 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34596, 76);

C2×(C31⋊C9)⋊D31 #46829316