C₂×#26039445 #37524518

order	22932
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂×#26039445

Splittings

derived, Hall	C₇²×C₁₃ ⋊ C₂²×C₉
Hall	#19153199 ⋊ C₂²
Hall	C₂×C₇⋊D₉₁ ⋊ C₉
Sylow	C₇² ⋊ C₂×D₁₃⋊C₉
Sylow	C₁₃ ⋊ C₂×#11725077

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	#16838447
commutator, hypocenter	C₇²×C₁₃	C₂²×C₉
Frattini	C₃	C₂×#16838447
Fitting, socle	C₂×C₃×C₇²×C₁₃	C₂×C₃
prime radical	C₂×C₃×C₇⋊D₉₁	C₃
cosocle	C₃×C₇²×C₁₃	C₂²×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₂×C₃

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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 463);

C2×#26039445 #37524518