Finite Group Databasebeta

C2×#13131098 #16806822

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13131098

Splittings

FittingC23×Q8×C13 ⋊ C4
SylowC13 ⋊ C2×#2123

Subgroups

subgroupG/H
centerC22C2×#88119
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC23×Q8×C13C4
socleC22×C13C2×#99
prime radicalC22×#6127C22
cosocleC2×C22⋊D13C24
hypercenterC23×Q8#261
hypocenterC13C2×#2123
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×Q8

1214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

166 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113471);