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C22⋊C4×D452 #28393397

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22⋊C4×D452

Splittings

FittingC4×C22⋊C4×C113 ⋊ C2
SylowC113 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
FittingC4×C22⋊C4×C113C2
socle, cosocleC23×C113C24
prime radicalC23×D452C2
hypercenterC4×C22⋊C4D113
hypocenterC113D4×C22⋊C4
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C4×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

2290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 7333);