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C5×#69207 #14315414

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

Aliases

direct productC5×#69207

Splittings

HallC3×C5 ⋊ C4×Q32
SylowC3 ⋊ C4×C5×Q32

Subgroups

subgroupG/H
centerC22×C5D3×D8
commutatorC3×C8C22×C4×C5
FrattiniC2×C8C22×C5×D3
FittingC3×C5×#358C2
socle, prime radicalC22×C3×C5C2×D8
cosocleC2×C3×C8C23×C5
hypercenterC5×#358D3
hypocenterC3C4×C5×Q32
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C5×#358

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 3 generators on 44 points:

(1,2,3,4,5)(7,8)(9,11,12,10);(6,7,8)(13,15,17,25)(14,19,21,35)(16,28,30,44)(18,33,29,26)(20,38,39,43)(22,40,32,36)(23,41,42,27)(24,37,34,31);(9,10,12,11)(13,14,17,21)(15,23,25,42)(16,27,30,41)(18,32,29,22)(19,34,35,24)(20,37,39,31)(26,43,33,38)(28,40,44,36)

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, 41112);