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C2×C3×D3×Dic6 #11724522

order864
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC2×C3×D3×Dic6

Splittings

SylowC33 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC22×C3C2×D32
commutator, cosocleC2×C32C24×C3
FrattiniC2C22×C3×D32
FittingC2×C33×C4C22
socleC22×C33C23
prime radicalC22×C32×D3C22
hypercenterC2×C3×C4D32
hypocenterC32C22×C3×Q8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#63560, D3×#63565, D3×#63566, …
maximal normal subgroup ofD3×#63560, D3×#63565, D3×#63566, …
maximal quotient ofC3×#10593860, C3×#10593861, C3×#10593859, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 4489);