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C8×C4⋊Dic15 #14296234

order1920
isoclinismisoclinic class of Dic30
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC8×C4⋊Dic15

Splittings

HallC3×C5 ⋊ C8×C4⋊C4
SylowC5 ⋊ C8×C4⋊Dic3
SylowC3 ⋊ C8×C4⋊Dic5

Subgroups

subgroupG/H
centerC22×C8C2×D15
commutatorC2×C3×C5C2×C4×C8
FrattiniC22×C4C22×D15
FittingC2×C3×C4×C5×C8C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4×C8D15
hypocenterC3×C5C8×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21932);