C₂₃×#3415 #15671034

order	2944
nilpotency class	4
isoclinism	isoclinic class of #3415
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#3415

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	C₂²×D₈
commutator, Frattini, cosocle	C₈	C₂⁴×C₂₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ #41×C₂₃ ◁ C₂₃×#131 ◁ G

370 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 180 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) = 55
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 4 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25)(26,31)(27,30)(28,41)(29,34)(32,38)(33,39)(35,45)(36,42)(37,51)(40,44)(43,52)(46,50)(47,49)(48,53)(54,55);(25,30)(27,38)(28,39)(31,42)(32,33)(34,44)(36,50)(37,49)(40,52)(41,43)(45,53)(46,47)(48,55)(51,54);(24,26)(25,31)(27,36)(28,37)(29,35)(30,42)(32,46)(33,47)(34,45)(38,50)(39,49)(40,48)(41,51)(43,54)(44,53)(52,55);(26,35)(31,45)(36,48)(37,49)(42,53)(46,54)(47,51)(50,55)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13669, C₂₃×#13671, C₂₃×#33854, …
maximal normal subgroup of	C₂₃×#13669, C₂₃×#13671, C₂₃×#33854, …
maximal quotient of	C₂₃×#33381, C₂₃×#33410, C₂₃×#33454, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2147);