C₇×C₃⋊D₃×C₂₃ #15668490

order	2898
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₂₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₇×C₃⋊D₃×C₂₃
unambiguous semidirect product	C₃⋊(D₃×C₇×C₂₃)

	subgroup	G/H
center, hypercenter	C₇×C₂₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₇×C₂₃

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1449

A minimal faithful permutation representation — 3 generators on 36 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2898, 29);