C₇×D₉×C₁₁⋊D₁₁ #44478958

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

Aliases

direct product	C₇×D₉×C₁₁⋊D₁₁
unambiguous semidirect product	(C₁₁×D₉)⋊(C₇×D₁₁)

Splittings

Fitting, Hall	C₇×C₉×C₁₁² ⋊ C₂²
derived, Hall	C₉×C₁₁² ⋊ C₂²×C₇
Hall	C₇×C₁₁² ⋊ C₂×D₉
Sylow	C₁₁² ⋊ C₂×C₇×D₉
Hall	C₇×C₉ ⋊ C₂×C₁₁⋊D₁₁
Sylow	C₉ ⋊ C₂×C₇×C₁₁⋊D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₇	D₉×C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₉×C₁₁²	C₂²×C₇
Frattini	C₃	D₃×C₇×C₁₁⋊D₁₁
Fitting	C₇×C₉×C₁₁²	C₂²
socle	C₃×C₇×C₁₁²	C₂×D₃
LCS	G ▷ C₉×C₁₁²
UCS	C₁ ◁ C₇

420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 7623

A minimal faithful permutation representation — 3 generators on 38 points:

(1,2,3,4,5,6,7)(8,13,11,10,15,12,14,9,16)(18,19)(20,21)(22,23)(24,25)(26,27)(29,30)(31,32)(33,34)(35,36)(37,38);(9,11)(10,14)(12,15)(13,16)(28,29,31,33,35,37,38,36,34,32,30);(17,18,20,22,24,26,27,25,23,21,19)

Conjugacy classes & character table

2604 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 181);

C7×D9×C11⋊D11 #44478958