C₂×C₁₃×C₇⋊D₆₃ #37524614

order	22932
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₂×C₁₃×C₇⋊D₆₃
unambiguous semidirect product	(C₂×C₇)⋊(C₁₃×D₆₃)
unambiguous semidirect product	(C₂×C₉)⋊(C₁₃×C₇⋊D₇)

Splittings

Fitting	C₂×C₇²×C₉×C₁₃ ⋊ C₂
derived, Hall	C₇²×C₉ ⋊ C₂²×C₁₃
Hall	C₇²×C₉×C₁₃ ⋊ C₂²
Hall	C₇²×C₁₃ ⋊ C₂×D₉
Hall	C₉×C₁₃ ⋊ C₂×C₇⋊D₇
Sylow	C₇² ⋊ C₂×C₁₃×D₉
Sylow	C₉ ⋊ C₂×C₁₃×C₇⋊D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₇⋊D₆₃
commutator, cosocle, hypocenter	C₇²×C₉	C₂²×C₁₃
Frattini	C₃	C₂×C₁₃×C₃⋊(C₇⋊D₇)
Fitting	C₂×C₇²×C₉×C₁₃	C₂
socle	C₂×C₃×C₇²×C₁₃	D₃
LCS	G ▷ C₇²×C₉
UCS	C₁ ◁ C₂×C₁₃

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 11466

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

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

Conjugacy classes & character table

5772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 559);

C2×C13×C7⋊D63 #37524614