Finite Group Databasebeta

C2×#20296023 #28379660

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20296023

Splittings

FittingC2×#41×C109 ⋊ C4
SylowC109 ⋊ C2×#421

Subgroups

subgroupG/H
centerC22C2×C22⋊#89137
commutatorC4×C109C23×C4
FrattiniC4C23×#89137
FittingC2×#41×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC2×#41×D109C2
cosocleC4×D109C24
hypercenterC2×#41#89137
hypocenterC109C2×#421
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21138);