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C5×#78458 #14415235

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

Aliases

direct productC5×#78458

Splittings

FittingC2×C3×C4×C5×C8 ⋊ C2
HallC3×C5 ⋊ #2931
SylowC3 ⋊ C5×#2931

Subgroups

subgroupG/H
centerC2×C5×C8C22×D3
commutatorC22×C3C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C4×C5×C8C2
socleC22×C3×C5C23×C4
prime radicalC5×#5477C2
cosocleC2×C3×C4C24×C5
hypercenterC2×C4×C5×C8D3
hypocenterC3C5×#2931
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C5×C8 ◁ C2×C4×C5×C8

1000 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)(13,16)(14,20)(15,22)(17,25)(18,24)(19,26)(21,27)(23,28);(13,15,17,23,18,14,19,21)(16,22,25,28,24,20,26,27);(7,8)(10,12)(16,24)(20,22)(25,26)(27,28);(7,8)(9,10)(11,12)(13,14,17,21,18,15,19,23)(16,22,25,28,24,20,26,27)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 140933);