Finite Group Databasebeta

C2×#13129894 #16789096

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13129894

Splittings

FittingC22×C13×C16 ⋊ C4
SylowC13 ⋊ C2×#1380

Subgroups

subgroupG/H
centerC23#88102
commutatorC8×C13C2×C42
FrattiniC2×C8C22×#261
FittingC22×C13×C16C4
socleC23×C13#107
prime radicalC23×D13D8
cosocleC2×C8×D13C23
hypercenterC22×C16#261
hypocenterC13C2×#1380
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1095745);