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C2×C23×#562 #15671146

order2944
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C25×C23 · Schur multiplier (H2) = C28

Aliases

direct productC2×C23×#562

Subgroups

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

1152 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);(4,7)(5,9)(11,12)(13,17)(14,15)(16,18);(4,7)(8,10)(12,15)(16,17);(3,4)(5,8)(6,7)(9,10)(11,13,14,18)(12,16,15,17);(3,5)(4,8)(6,9)(7,10)(11,12)(13,16)(14,15)(17,18)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#8508, C2×C23×#1656, C2×C23×#1661, …
maximal normal subgroup ofC23×#8508, C2×C23×#1656, C2×C23×#1661, …
maximal quotient ofC2×C23×#2376, C2×C23×#2377, C2×C23×#2378, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2259);