Finite Group Databasebeta

← Prev (#11746155) Next (#11746157) →

C5×#4457 #11746156

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

Aliases

direct productC5×#4457

Splittings

HallC3×C5 ⋊ #334
SylowC3 ⋊ C5×#334

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×#334
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)(17,18,19,21,20,22,23,24);(7,8)(9,10,11,13,12,14,15,16)(18,21)(19,23)(22,24)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#67762, C5×#67516, #14277854, …
maximal normal subgroup ofC5×#67762, C5×#67516, #14277854, …
maximal quotient ofC5×#67654, C5×#67439, C5×#67513, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 351);