C₂×C₃×#16838447 #37525466

order	22932
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product

C₂×C₃×#16838447

Splittings

Fitting, socle	C₂×C₃×C₇²×C₁₃ ⋊ C₂×C₃
derived, Hall	C₇²×C₁₃ ⋊ C₂²×C₃²
Hall	C₃×#14274262 ⋊ C₂²
Hall	C₂×C₇⋊D₉₁ ⋊ C₃²
Sylow	C₇² ⋊ C₂×C₃×D₁₃⋊C₃
Sylow	C₁₃ ⋊ C₂×C₃×#64424

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	#16838447
commutator, cosocle, hypocenter	C₇²×C₁₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₂×C₃

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 3822

A minimal faithful permutation representation — 3 generators on 32 points:

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

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, 1411);

C2×C3×#16838447 #37525466