Finite Group Databasebeta

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C23×#809 #11658694

order768
isoclinismisoclinic class of #213
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×#809

Splittings

FittingC23×C3×C4⋊C4 ⋊ C2
SylowC3 ⋊ C23×#102

Subgroups

subgroupG/H
centerC25#67
commutatorC3×C4C24×C4
FrattiniC2×C4C24×D3
FittingC23×C3×C4⋊C4C2
socleC25×C3D4
prime radicalC24×D12C2
cosocleC2×C3×C4C25
hypercenterC23×C4⋊C4D3
hypocenterC3C23×#102
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1033075);