C₂×C₇×C₉⋊(C₁₁⋊D₁₁) #44478987

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

Aliases

direct product	C₂×C₇×C₉⋊(C₁₁⋊D₁₁)
unambiguous semidirect product	(C₂×C₉)⋊(C₇×C₁₁⋊D₁₁)
unambiguous semidirect product	(C₂×C₁₁)⋊(C₇×D₉₉)

Splittings

Fitting	C₂×C₇×C₉×C₁₁² ⋊ C₂
derived, Hall	C₉×C₁₁² ⋊ C₂²×C₇
Hall	C₇×C₉×C₁₁² ⋊ C₂²
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	C₂×C₇	C₉⋊(C₁₁⋊D₁₁)
commutator, cosocle, hypocenter	C₉×C₁₁²	C₂²×C₇
Frattini	C₃	C₂×C₇×C₃⋊(C₁₁⋊D₁₁)
Fitting	C₂×C₇×C₉×C₁₁²	C₂
socle	C₂×C₃×C₇×C₁₁²	D₃
LCS	G ▷ C₉×C₁₁²
UCS	C₁ ◁ C₂×C₇

420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 15246

A minimal faithful permutation representation — 3 generators on 40 points:

(3,4,5,6,7,8,9)(11,13)(12,16)(14,15)(17,18)(20,21)(22,23)(24,25)(26,27)(28,29)(31,32)(33,34)(35,36)(37,38)(39,40);(1,2)(10,18,13,16,15,14,12,11,17)(30,31,33,35,37,39,40,38,36,34,32);(19,20,22,24,26,28,29,27,25,23,21)

Conjugacy classes & character table

7644 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 210);

C2×C7×C9⋊(C11⋊D11) #44478987