C₉×D₇×C₁₁⋊D₁₁ #44478953

order	30492
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₁₁

Aliases

direct product

C₉×D₇×C₁₁⋊D₁₁

Splittings

Fitting, Hall	C₇×C₉×C₁₁² ⋊ C₂²
derived, Hall	C₇×C₁₁² ⋊ C₂²×C₉
Hall	C₉×C₁₁² ⋊ C₂×D₇
Sylow	C₁₁² ⋊ C₂×C₉×D₇
Hall	C₇×C₉ ⋊ C₂×C₁₁⋊D₁₁
Sylow	C₇ ⋊ C₂×C₉×C₁₁⋊D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₇×C₁₁⋊D₁₁
commutator, hypocenter	C₇×C₁₁²	C₂²×C₉
Frattini	C₃	C₃×D₇×C₁₁⋊D₁₁
Fitting	C₇×C₉×C₁₁²	C₂²
socle, cosocle	C₃×C₇×C₁₁²	C₂²×C₃
prime radical	C₃×D₇×C₁₁⋊D₁₁	C₃
LCS	G ▷ C₇×C₁₁²
UCS	C₁ ◁ C₉

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:

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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 176);

C9×D7×C11⋊D11 #44478953