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C2×C4×C3⋊#672 #14312511

order1920
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×C3⋊#672

Splittings

derived, HallC3×C5 ⋊ C2×C4×C16
SylowC5 ⋊ C2×C4×C3⋊C16
SylowC3 ⋊ C2×C4×#672

Subgroups

subgroupG/H
center, hypercenterC2×C4×C8D15
commutator, hypocenterC3×C5C2×C4×C16
FrattiniC2×C8C22×D15
FittingC2×C3×C4×C5×C8C2
socle, prime radicalC23×C3×C5C2×C8
cosocleC2×C3×C5×C8C23
LCSG ▷ C3×C5
UCSC1 ◁ C2×C4×C8

432 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, 38209);