C₇×(C₃⋊D₃)⋊(C₁₁⋊D₁₁) #44479212

order	30492
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂×C₁₁

Aliases

direct product	C₇×(C₃⋊D₃)⋊(C₁₁⋊D₁₁)
unambiguous semidirect product	(C₃⋊D₃)⋊(C₇×C₁₁⋊D₁₁)

Splittings

Fitting, socle, Hall	C₃²×C₇×C₁₁² ⋊ C₂²
derived, Hall	C₃²×C₁₁² ⋊ C₂²×C₇
Hall	C₇×C₁₁² ⋊ D₃²
Sylow	C₁₁² ⋊ D₃²×C₇
Hall	C₃²×C₇ ⋊ C₂×C₁₁⋊D₁₁
Sylow	C₃² ⋊ C₂×C₇×C₁₁⋊D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₇	(C₃⋊D₃)⋊(C₁₁⋊D₁₁)
commutator, cosocle, hypocenter	C₃²×C₁₁²	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁²	C₂²
LCS	G ▷ C₃²×C₁₁²
UCS	C₁ ◁ C₇

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 5082

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7)(9,10)(11,12)(25,26,28,30,32,34,35,33,31,29,27);(8,9,10)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(26,27)(28,29)(30,31)(32,33)(34,35);(14,15,17,19,21,23,24,22,20,18,16)

Conjugacy classes & character table

2583 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 435);

C7×(C3⋊D3)⋊(C11⋊D11) #44479212