C₂×#26039450 #37524523

order	22932
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product

C₂×#26039450

Splittings

derived, Hall	C₇²×C₁₃ ⋊ C₂²×C₉
Hall	C₁₃⋊#89205 ⋊ C₂²
Hall	C₂×C₇⋊D₉₁ ⋊ C₉
Sylow	C₇² ⋊ C₂×D₁₃⋊C₉
Sylow	C₁₃ ⋊ C₂×#11725078

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	#16838452
commutator, hypocenter	C₇²×C₁₃	C₂²×C₉
Frattini	C₃	C₂×#16838452
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

160 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 1638

A minimal faithful permutation representation — 2 generators on 38 points:

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

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, 468);