Finite Group Databasebeta

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C5×#70236 #14300014

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#70236

Splittings

HallC3×C5 ⋊ #1863
SylowC3 ⋊ C5×#1863

Subgroups

subgroupG/H
centerC23×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×#103C2
socle, prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×#103D3
hypocenterC3C5×#1863
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C22×C4×C5 ◁ C2×C5×#103

596 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 25712);