Finite Group Databasebeta

C2×#20295000 #28371489

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

Aliases

direct productC2×#20295000

Splittings

SylowC109 ⋊ C2×#410

Subgroups

subgroupG/H
centerC2×C4C22⋊Dic109
commutatorC22×C109C23×C4
FrattiniC23C23×D109
Fitting, prime radicalC22×#41×C109C2
socleC22×C109C2×C22⋊C4
cosocleC23×C109C24
hypercenterC22×#41D109
hypocenterC109C2×#410
LCSG ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

2204 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 12967);