Finite Group Databasebeta

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C4⋊C4×D13⋊C8 #16797119

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4⋊C4×D13⋊C8

Splittings

SylowC13 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C22×C4×C8
FrattiniC23C23×#261
FittingC4×C13×C4⋊C4C4
socleC23×C13C23×C4
prime radicalC23×D13C22×C4
cosocleC22×Dic13C24
hypercenterC4×C4⋊C4#261
hypocenterC13C2×C8×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103768);