C₇×((C₁₁⋊D₁₁)⋊C₃)⋊D₃ #44479090

order	30492
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₇×((C₁₁⋊D₁₁)⋊C₃)⋊D₃
unambiguous semidirect product	((C₁₁⋊D₁₁)⋊C₃)⋊(D₃×C₇)

Splittings

Fitting, socle	C₃×C₇×C₁₁² ⋊ C₂×D₃
derived, Hall	C₃×C₁₁²⋊C₃ ⋊ C₂²×C₇
Hall	C₃×C₇×C₁₁²⋊C₃ ⋊ C₂²
Hall	C₇×C₁₁² ⋊ C₂×C₃⋊D₃
Sylow	C₁₁² ⋊ C₂×C₇×C₃⋊D₃

Subgroups

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

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 693

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7)(8,9,10)(11,13)(12,16)(14,32)(18,20)(19,21)(22,39)(23,40)(24,25)(26,28)(27,29)(30,37)(31,35)(33,34)(36,38)(41,42);(9,10)(12,15)(13,18)(14,20)(16,24)(17,27)(19,25)(21,33)(22,37)(23,36)(26,41)(28,29)(30,32)(31,34)(35,40)(38,42)(39,43);(11,12,15)(13,19,24)(14,21,34)(16,25,18)(17,29,39)(20,31,33)(22,38,41)(23,30,35)(26,42,37)(27,43,28)(32,36,40)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 313);

C7×((C11⋊D11)⋊C3)⋊D3 #44479090