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C5×#4458 #11746157

order960
isoclinismisoclinic class of #204
automorphism?
homologyAbelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2

Aliases

direct productC5×#4458

Splittings

HallC3×C5 ⋊ #335
SylowC3 ⋊ C5×#335

Subgroups

subgroupG/H
centerC2×C4×C5D12
commutatorC3×C4C2×C5×C8
FrattiniC42C2×C5×D3
FittingC3×C4×C5×C8C2
socle, prime radicalC22×C3×C5C4⋊C4
cosocleC3×C42C22×C5
hypercenterC4×C5×C8D3
hypocenterC3C5×#335
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C42×C5 ◁ C4×C5×C8

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×#67763, C5×#67504, #14277808, …
maximal normal subgroup ofC5×#67763, C5×#67504, #14277808, …
maximal quotient ofC5×#67654, C5×#67440, C5×#67500, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 352);