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C23×A5 #13063406

order1380
isoclinismisoclinic class of A5
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C2

Aliases

direct productC23×A5

Subgroups

subgroupG/H
center, Fitting, hypercenterC23A5
commutator, hypocenterA5C23
FrattiniC1G
LCSG ▷ A5
UCSC1 ◁ C23

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 115

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28);(24,25,26)

Conjugacy classes & character table

115 conjugacy classes — view the full character table.

Relationships

derived subgroup ofA5×C23⋊C11
socle ofA5×C23⋊C11, A5×C529
maximal subgroup ofC3×C23×A5, C11×C23×A5, A5×C23⋊C11, …
maximal normal subgroup ofC3×C23×A5, C11×C23×A5, A5×C23⋊C11, …
maximal quotient ofC3×C23×A5, C11×C23×A5, C13×C23×A5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1380, 9);