C₂₃×#3359 #15670978

order	2944
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#3359

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂×D₄×C₂₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×Q₈×C₂₃ ◁ G

370 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 192 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)(25,28)(29,30)(32,33,35,38)(34,36,39,37);(24,25,27,28)(26,30,31,29);(33,36)(34,39)(37,38);(24,26,27,31)(25,29,28,30)

Conjugacy classes & character table

805 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#19764, C₂₃×#19769, C₂₃×#19795, …
maximal normal subgroup of	C₂₃×#19764, C₂₃×#19769, C₂₃×#19795, …
maximal quotient of	Q₈×C₂₃×#102, C₂₃×#22542, C₂₃×#22738, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2091);