Finite Group Databasebeta

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C2×C23×#534 #15671064

order2944
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C25×C23 · Schur multiplier (H2) = C29

Aliases

direct productC2×C23×#534

Subgroups

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

1984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 736

A minimal faithful permutation representation — 5 generators on 37 points:

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

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#8403, C23×#10972, C23×#10995, …
maximal normal subgroup ofC23×#8403, C23×#10972, C23×#10995, …
maximal quotient ofC2×C23×#2308, C2×C23×#2315, C2×C23×#2321, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2177);