Finite Group Databasebeta

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C5×#69926 #14298499

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

Aliases

direct productC5×#69926

Splittings

HallC3×C5 ⋊ #1825
SylowC3 ⋊ C5×#1825

Subgroups

subgroupG/H
centerC23×C5C2×D12
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×C22⋊C8C2
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×C22⋊C8D3
hypocenterC3C5×#1825
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ C2×C5×C22⋊C8

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24197);