C₂₃×#1437 #15669056

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₂₃×#1437

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

828 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 828 conjugacy classes of subgroups — too many to draw. Only its 280 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 — 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)(28,29,31,30)(33,34)(36,37,39,38);(32,33,35,34)(36,37,39,38);(24,25,26,27)(28,30,31,29)(32,34,35,33)(36,38,39,37)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7213, C₂₃×#8346, C₂×C₂₃×#1437, …
maximal normal subgroup of	C₂₃×#7213, C₂₃×#8346, C₂×C₂₃×#1437, …
maximal quotient of	C₂₃×#7554, C₂₃×#7555, C₂₃×#7556, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 169);