Finite Group Databasebeta

C2×#20295975 #28379484

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20295975
unambiguous semidirect productD109⋊#387

Splittings

FittingC2×C4⋊C4×C109 ⋊ C4
SylowC109 ⋊ C2×#387

Subgroups

subgroupG/H
centerC23C22×#89137
commutatorC22×C109C23×C4
FrattiniC22C23×#89137
FittingC2×C4⋊C4×C109C4
socleC23×C109C22×C4
prime radicalC23×D109C23
cosocleC22×D109C24
hypercenterC2×C4⋊C4#89137
hypocenterC109C2×#387
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C2×C4⋊C4

712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

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(13952, 20962);