C₁₃×D₇×C₃⋊D₂₁ #37525637

order	22932
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₁₃×D₇×C₃⋊D₂₁
unambiguous semidirect product	(C₃×D₇)⋊(C₁₃×D₂₁)
unambiguous semidirect product	(C₇×D₇)⋊(C₁₃×C₃⋊D₃)

	subgroup	G/H
center, hypercenter	C₁₃	D₇×C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇²	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₂²
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₁₃

312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

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

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1638

A minimal faithful permutation representation — 3 generators on 33 points:

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

2145 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 1582);