Finite Group Databasebeta

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C4×C8×Dic15 #14294184

order1920
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C43

Aliases

direct productC4×C8×Dic15

Splittings

derived, HallC3×C5 ⋊ C42×C8
SylowC5 ⋊ C4×C8×Dic3
SylowC3 ⋊ C4×C8×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C4×C8D15
commutator, hypocenterC3×C5C42×C8
FrattiniC22×C4C22×D15
FittingC2×C3×C4×C5×C8C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4×C5C23
LCSG ▷ C3×C5
UCSC1 ◁ C2×C4×C8

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 19882);