Finite Group Databasebeta

C2×#20295068 #28371617

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

Aliases

direct productC2×#20295068

Splittings

SylowC109 ⋊ C2×#428

Subgroups

subgroupG/H
centerC23C2×D436
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
FittingC22×M16×C109C2
socleC23×C109C2×D4
prime radicalC24×C109D4
cosocleC2×C4×C109C24
hypercenterC22×M16D109
hypocenterC109C2×#428
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

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, 13095);