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Cayley diagram

C2×C5×D23 #90750

order460
isoclinismisoclinic class of D23
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D23
unambiguous semidirect productC23⋊(C22×C5)
unambiguous semidirect product(C2×C23)⋊(C2×C5)

Splittings

Fitting, socleC2×C5×C23 ⋊ C2
derived, SylowC23 ⋊ C22×C5
HallC5×C23 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C5D23
commutator, cosocle, hypocenterC23C22×C5
FrattiniC1G
Fitting, socleC2×C5×C23C2
LCSG ▷ C23
UCSC1 ◁ C2×C5

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 230

A minimal faithful permutation representation — 2 generators on 30 points:

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

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×D23, #11745065, #11745066, …
maximal normal subgroup ofDic5×D23, #11745065, #11745066, …
maximal quotient ofC5×Dic46, C4×C5×D23, C5×D92, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(460, 8);