Finite Group Databasebeta

C23×#88237 #16809627

order3328
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4

Aliases

direct productC23×#88237
unambiguous semidirect productD13⋊(C22×#117)

Splittings

FittingC24×C4×C13 ⋊ C4
SylowC13 ⋊ C23×#117

Subgroups

subgroupG/H
centerC23×C4C2×#261
commutatorC2×C13C25×C4
FrattiniC2C25×#261
FittingC24×C4×C13C4
socleC24×C13C22×C4
prime radicalC25×D13C22
cosocleC2×D13C26
hypercenterC24×C4#261
hypocenterC13C23×#117
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C24×C4

14334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1116276);