D₃×#16838457 #37525290

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

Aliases

direct product

D₃×#16838457

Splittings

Fitting, socle, derived	C₃×C₇²×C₁₃ ⋊ C₂²×C₃
Hall	C₃×#14274262 ⋊ C₂²
Hall	C₇²×C₁₃ ⋊ C₂×C₃×D₃
Sylow	C₇² ⋊ D₃×D₁₃⋊C₃
Sylow	C₁₃ ⋊ D₃×#64423

Subgroups

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

230 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 39 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) = 30
transitive degree	μ_t(G) = 546

A minimal faithful permutation representation — 2 generators on 30 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 1235);