Finite Group Databasebeta

C2×#20295976 #28379485

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20295976
unambiguous semidirect productD109⋊#388

Splittings

FittingC2×C22⋊C4×C109 ⋊ C4
SylowC109 ⋊ C2×#388

Subgroups

subgroupG/H
centerC23C22×#89137
commutatorC22×C109C23×C4
FrattiniC22C23×#89137
FittingC2×C22⋊C4×C109C4
socleC23×C109C22×C4
prime radicalC24×D109C22
cosocleC22×D109C24
hypercenterC2×C22⋊C4#89137
hypocenterC109C2×#388
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C2×C22⋊C4

928 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, 20963);