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C2×C23×#538 #15671069

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

Aliases

direct productC2×C23×#538

Subgroups

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

1336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 736

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

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#8408, C23×#17386, C23×#17405, …
maximal normal subgroup ofC23×#8408, C23×#17386, C23×#17405, …
maximal quotient ofC2×C23×#2312, C2×C23×#2318, C2×C23×#2321, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2182);