C₂₃×#2501 #15670120

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₃×#2501

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#121	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

708 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 248 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) = 39
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 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)(25,26)(29,30)(32,33,36,38)(34,35,37,39);(24,25,27,26)(28,29,31,30)(32,34)(33,35)(36,37)(38,39);(28,29,31,30)(32,35)(33,37)(34,38)(36,39);(24,26,27,25)(28,30,31,29)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9464, C₂₃×#9952, C₂₃×#9960, …
maximal normal subgroup of	C₂₃×#9464, C₂₃×#9952, C₂₃×#9960, …
maximal quotient of	C₂₃×#13880, C₂₃×#13904, C₂₃×#13996, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1233);