Finite Group Databasebeta

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C4×#22575413 #46813229

order34432
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#22575413

Splittings

FittingC4×C22⋊C4×C269 ⋊ C2
SylowC269 ⋊ C42×D4

Subgroups

subgroupG/H
centerC22×C4C22×D269
commutatorC2×C269C22×C42
FrattiniC23C23×D269
FittingC4×C22⋊C4×C269C2
socle, cosocleC23×C269C24
prime radicalC22×C22⋊D269C22
hypercenterC4×C22⋊C4D269
hypocenterC269C42×D4
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

924 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

5440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 6854);