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C5×C4⋊C4×C3⋊C8 #14296238

order1920
automorphism?
homologyAbelianization (H1) = C2×C4×C5×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC5×C4⋊C4×C3⋊C8

Splittings

HallC3×C5 ⋊ C8×C4⋊C4
SylowC3 ⋊ C5×C8×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4×C5C22×D3
commutatorC2×C3C2×C4×C5×C8
FrattiniC22×C4C22×C5×D3
FittingC3×C4×C5×C4⋊C4C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4C23×C5
hypercenterC4×C5×C4⋊C4D3
hypocenterC3C5×C8×C4⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C4×C5×C4⋊C4

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21936);