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C5×#78574 #14417740

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#78574

Splittings

FittingC3×C5×#405 ⋊ C2
HallC3×C5 ⋊ #2952
SylowC3 ⋊ C5×#2952

Subgroups

subgroupG/H
centerC22×C5C22×D12
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#405C2
socleC22×C3×C5C22×D4
prime radicalC2×C5×#904C2
cosocleC2×C3×C4C24×C5
hypercenterC5×#405D3
hypocenterC3C5×#2952
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#117 ◁ C5×#405

968 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 143438);