Finite Group Databasebeta

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C22×C4×#92314 #72268930

order7776
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26×C3

Aliases

direct productC22×C4×#92314

Splittings

FittingC22×C4×#6900 ⋊ C2
derivedC92 ⋊ C23×C3×C4
Sylow#6900 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC22×C4#92314
commutator, hypocenterC92C23×C3×C4
FrattiniC2×C32C23×C3×C3⋊D3
FittingC22×C4×#6900C2
socleC23×C32C2×C3×C3⋊D3
prime radicalC23×#92314C2
cosocleC2×C92C24×C3
LCSG ▷ C92
UCSC1 ◁ C22×C4

5752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1296

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.