Finite Group Databasebeta

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C4×#22575452 #46813455

order34432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#22575452

Splittings

SylowC269 ⋊ C4×C4⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D269
commutatorC22×C269C23×C4
FrattiniC23C23×D269
FittingC4×C4⋊C4×C269C2
socle, prime radical, cosocleC23×C269C24
hypercenterC4×C4⋊C4D269
hypocenterC269C4×C4⋊Q8
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34432

Conjugacy classes & character table

5416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 7080);