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Q8×C4⋊Dic15 #14327222

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

Aliases

direct productQ8×C4⋊Dic15

Splittings

HallC3×C5 ⋊ Q8×C4⋊C4
SylowC5 ⋊ Q8×C4⋊Dic3
SylowC3 ⋊ Q8×C4⋊Dic5

Subgroups

subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC2×C3×C4×C5×Q8C2
socle, prime radical, cosocleC23×C3×C5C24
hypercenterC2×C4×Q8D15
hypocenterC3×C5Q8×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4×Q8

1136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 52920);