Finite Group Databasebeta

C2×#20296036 #28379683

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

Aliases

direct productC2×#20296036
unambiguous semidirect productD109⋊#427

Splittings

FittingC22×C8×C109 ⋊ C4
SylowC109 ⋊ C2×#427

Subgroups

subgroupG/H
centerC2×C4C4⋊#89137
commutatorC4×C109C23×C4
FrattiniC4C23×#89137
FittingC22×C8×C109C4
socleC22×C109C2×C4⋊C4
prime radicalC23×D109D4
cosocleC4×D109C24
hypercenterC22×C8#89137
hypocenterC109C2×#427
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21161);