Finite Group Databasebeta

C2×#13131437 #16808070

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13131437

Splittings

FittingC23×Q8×C13 ⋊ C4
SylowC13 ⋊ C2×#2884

Subgroups

subgroupG/H
centerC22C22×C22⋊#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC23×Q8×C13C4
socleC22×C13C22×C22⋊C4
prime radicalC22×#88254C2
cosocleC22×D13C25
hypercenterC23×Q8#261
hypocenterC13C2×#2884
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×Q8 ◁ C23×Q8

4818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

202 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114719);