Finite Group Databasebeta

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C4⋊C8×D397 #38762541

order25408
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C8×D397

Splittings

FittingC4⋊C8×C397 ⋊ C2
SylowC397 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D397
commutatorC2×C397C22×C8
FittingC4⋊C8×C397C2
socleC22×C397C22×C4
prime radicalC22×D397C2×C4
cosocleC2×C4×C397C23
hypercenterC4⋊C8D397
hypocenterC397C2×C4⋊C8
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C2×C4 ◁ C4⋊C8

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

4000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 568);