Finite Group Databasebeta

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C2×C3×Dic3×C4⋊C4 #11800729

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C3×Dic3×C4⋊C4

Splittings

SylowC32 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24×C3C22×D3
commutatorC2×C3C22×C3×C42
FrattiniC23C23×C3×D3
FittingC22×C32×C4⋊C4C2
socle, prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C2×C3×C4×C4⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C4⋊C4

2065 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 34740);