Finite Group Databasebeta

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C2×C3×C4×#672 #14312510

order1920
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C3×C4×#672

Splittings

derived, SylowC5 ⋊ C2×C3×C4×C16
HallC3×C5 ⋊ C2×C4×C16

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4×C8D5
commutator, hypocenterC5C2×C3×C4×C16
FrattiniC2×C8C22×C3×D5
FittingC2×C3×C4×C5×C8C2
socle, prime radicalC23×C3×C5C2×C8
cosocleC2×C5×C8C23×C3
LCSG ▷ C5
UCSC1 ◁ C2×C3×C4×C8

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38208);