Finite Group Databasebeta

C23×#88049 #16726426

order3328
isoclinismisoclinic class of #6104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×#88049

Splittings

FittingC23×C13×C4⋊C4 ⋊ C2
SylowC13 ⋊ C23×#102

Subgroups

subgroupG/H
centerC25C22⋊D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC23×C13×C4⋊C4C2
socleC25×C13D4
prime radicalC24×D52C2
cosocleC2×C4×C13C25
hypercenterC23×C4⋊C4D13
hypocenterC13C23×#102
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033075);