Finite Group Databasebeta

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C4×#16813580 #28392914

order14464
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#16813580

Splittings

FittingC4×C4⋊C4×C113 ⋊ C2
SylowC113 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D113
commutatorC2×C113C22×C42
FrattiniC23C23×D113
FittingC4×C4⋊C4×C113C2
socle, cosocleC23×C113C24
prime radicalC23×D113C23
hypercenterC4×C4⋊C4D113
hypocenterC113C4×#117
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 6850);