Finite Group Databasebeta

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C2×#20290828 #28320241

order13568
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20290828
unambiguous semidirect productD53⋊#1949

Splittings

FittingC2×C4⋊C8×C53 ⋊ C4
SylowC53 ⋊ C2×#1949

Subgroups

subgroupG/H
centerC23C2×C4⋊#6157
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC2×C4⋊C8×C53C4
socleC23×C53C2×C4⋊C4
prime radicalC23×D53C2×D4
cosocleC2×C4×D53C24
hypercenterC2×C4⋊C8#6157
hypocenterC53C2×#1949
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

1142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1105717);