Finite Group Databasebeta

C23×#13182038 #28380017

order13952
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC23×#13182038

Splittings

SylowC109 ⋊ C23×M16

Subgroups

subgroupG/H
centerC24C2×#89137
commutatorC2×C109C24×C4
FrattiniC2C24×#89137
Fitting, prime radicalC25×C109C4
socleC24×C109C2×C4
cosocleDic109C25
hypercenterC25#89137
hypocenterC109C23×M16
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C24 ◁ C25

1720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21495);