C₂₃×C₂²⋊#95 #15669052

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product	C₂₃×C₂²⋊#95
unambiguous semidirect product	C₂²⋊(C₂₃×#95)

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂³
commutator	C₂²	C₂×C₄²×C₂₃
Frattini, cosocle	C₂⁴	C₂³×C₂₃
prime radical	C₂⁵×C₂₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

1088 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(28,29,30,31)(33,35);(32,33)(34,35)(36,37,38,39);(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#7032, C₂₃×#7035, C₂₃×#7187, …
maximal normal subgroup of	C₂₃×#7032, C₂₃×#7035, C₂₃×#7187, …
maximal quotient of	C₂₃×#7554, C₂₃×#7555, C₂₃×#7557, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 165);

C23×C22⋊#95 #15669052