Finite Group Databasebeta

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C4×#16813607 #28393100

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#16813607

Splittings

FittingC4×C4⋊C4×C113 ⋊ C2
SylowC113 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D113
commutatorC22×C113C23×C4
FrattiniC23C23×D113
FittingC4×C4⋊C4×C113C2
socle, cosocleC23×C113C24
prime radicalC22×D452C22
hypercenterC4×C4⋊C4D113
hypocenterC113C4×#123
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 7036);