C₃²×D₇×C₁₁⋊D₁₁ #44479185

order	30492
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃×C₁₁

Aliases

direct product

C₃²×D₇×C₁₁⋊D₁₁

Splittings

Fitting, socle, Hall	C₃²×C₇×C₁₁² ⋊ C₂²
derived, Hall	C₇×C₁₁² ⋊ C₂²×C₃²
Hall	C₃²×C₁₁² ⋊ C₂×D₇
Sylow	C₁₁² ⋊ C₂×C₃²×D₇
Hall	C₃²×C₇ ⋊ C₂×C₁₁⋊D₁₁
Sylow	C₇ ⋊ C₂×C₃²×C₁₁⋊D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃²	D₇×C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₇×C₁₁²	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁²	C₂²
LCS	G ▷ C₇×C₁₁²
UCS	C₁ ◁ C₃²

840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 7623

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

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

Conjugacy classes & character table

2790 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 408);

C32×D7×C11⋊D11 #44479185