Finite Group Databasebeta

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C2×C23×#544 #15671076

order2944
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C25×C23 · Schur multiplier (H2) = C28

Aliases

direct productC2×C23×#544

Subgroups

subgroupG/H
center, socleC23×C23C24
commutator, Frattini, cosocleC22C25×C23
prime radicalC24×C23C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C23 ◁ G

1080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 1472

A minimal faithful permutation representation — 5 generators on 41 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(3,4)(5,9)(6,8)(7,10)(11,12,14,16)(13,17,18,15);(3,4,6,8)(5,7,10,9);(3,4)(5,7)(6,8)(9,10)(11,13,14,18)(12,15,16,17);(3,5)(4,7)(6,10)(8,9)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#8406, C23×#8525, C23×#11388, …
maximal normal subgroup ofC23×#8406, C23×#8525, C23×#11388, …
maximal quotient ofC2×C23×#2316, C2×C23×#2317, C2×C23×#2329, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2189);