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C5×#71644 #14298584

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

Aliases

direct productC5×#71644

Splittings

HallC3×C5 ⋊ #1827
SylowC3 ⋊ C5×#1827

Subgroups

subgroupG/H
centerC4×C5#926
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C4×C5×#41C2
socleC2×C3×C5#381
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4C23×C5
hypercenterC4×C5×#41D3
hypocenterC3C5×#1827
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C5×#117 ◁ C4×C5×#41

524 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24282);