Finite Group Databasebeta

C23×#88238 #16809646

order3328
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC23×#88238

Splittings

SylowC13 ⋊ C23×#131

Subgroups

subgroupG/H
centerC24C22×#261
commutatorC2×C13C25×C4
FrattiniC2C25×#261
FittingC23×D4×C13C4
socleC24×C13C22×C4
prime radicalC23×#6129C2
cosocleDic13C26
hypercenterC23×D4#261
hypocenterC13C23×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×D4

11422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1116295);