Finite Group Databasebeta

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C3×C4×#3968 #14295460

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×C4×#3968

Splittings

HallC3×C5 ⋊ C4×#101
SylowC5 ⋊ C3×C4×#101

Subgroups

subgroupG/H
centerC2×C3×C4C22⋊Dic5
commutatorC22×C5C2×C3×C42
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C4×C5×Q8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22×C4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C4×Q8D5
hypocenterC5C3×C4×#101
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4×Q8

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21158);