Finite Group Databasebeta

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C2×C4⋊C4×Dic269 #46813222

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

Aliases

direct productC2×C4⋊C4×Dic269

Splittings

SylowC269 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×D269
commutatorC2×C269C22×C42
FrattiniC23C23×D269
FittingC22×C4⋊C4×C269C2
socle, prime radicalC24×C269C23
cosocleC23×C269C24
hypercenterC22×C4⋊C4D269
hypocenterC269C2×C4×C4⋊C4
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C24 ◁ C22×C4⋊C4

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34432

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, 6847);