Finite Group Databasebeta

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C5×#70681 #14299778

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

Aliases

direct productC5×#70681

Splittings

FittingC3×C5×#428 ⋊ C2
HallC3×C5 ⋊ #1860
SylowC3 ⋊ C5×#1860

Subgroups

subgroupG/H
centerC22×C5#937
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#428C2
socleC22×C3×C5#120
prime radicalC2×C5×#235C22
cosocleC22×C3×C4C23×C5
hypercenterC5×#428D3
hypocenterC3C5×#1860
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#428

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 25476);