Finite Group Databasebeta

C2×#20296084 #28379996

order13952
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20296084

Splittings

SylowC109 ⋊ C2×#504

Subgroups

subgroupG/H
centerC2×C4C22×#89137
commutatorC2×C109C23×C8
FrattiniC4C23×#89137
Fitting, prime radicalC2×#41×C109C4
socleC22×C109C22×C8
cosocle#11724784C24
hypercenterC2×#41#89137
hypocenterC109C2×#504
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C2×#41

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21474);