Finite Group Databasebeta

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C5×#82207 #14413404

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

Aliases

direct productC5×#82207

Splittings

HallC3×C5 ⋊ #2911
SylowC3 ⋊ C5×#2911

Subgroups

subgroupG/H
centerC2×C4×C5C2×#67
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×#117C2
socleC22×C3×C5C22×D4
prime radicalC24×C3×C5D4
cosocleC2×C3×C4C24×C5
hypercenterC2×C5×#117D3
hypocenterC3C5×#2911
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C23×C4×C5 ◁ C2×C5×#117

984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

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, 139102);