D₇⋊C₉×C₁₁⋊D₁₁ #44478922

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

Aliases

direct product	D₇⋊C₉×C₁₁⋊D₁₁
unambiguous semidirect product	D₇⋊(C₉×C₁₁⋊D₁₁)
unambiguous semidirect product	(C₁₁×D₇⋊C₉)⋊D₁₁

Splittings

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

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	AGL(1,𝔽₇)×C₁₁⋊D₁₁
commutator, hypocenter	C₇×C₁₁²	C₂²×C₉
Fitting, socle, cosocle	C₃×C₇×C₁₁²	C₂²×C₃
prime radical	C₃×D₇×C₁₁⋊D₁₁	C₃
LCS	G ▷ C₇×C₁₁²
UCS	C₁ ◁ C₃

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:

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

1302 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 145);

D7⋊C9×C11⋊D11 #44478922