Finite Group Databasebeta

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C5×#69724 #14280435

order1920
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C2×C4×C5×C8 · Schur multiplier (H2) = C2×C8

Aliases

direct productC5×#69724

Splittings

HallC3×C5 ⋊ #1450
SylowC3 ⋊ C5×#1450

Subgroups

subgroupG/H
centerC4×C5×C8C2×D3
commutatorC2×C3C2×C4×C5×C8
FrattiniC42C22×C5×D3
FittingC2×C3×C4×C5×C8C2
socleC22×C3×C5C2×C42
prime radicalC23×C3×C5C42
cosocleC3×C42C23×C5
hypercenterC2×C4×C5×C8D3
hypocenterC3C5×#1450
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5×C8 ◁ C2×C4×C5×C8

424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6133);