Finite Group Databasebeta

C2×#13123674 #16727023

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13123674

Splittings

FittingC2×C4×C13×Q16 ⋊ C2
SylowC13 ⋊ C2×#2947

Subgroups

subgroupG/H
centerC23C2×D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C4×C13×Q16C2
socleC23×C13C22×D4
prime radicalC22×#6131C22
cosocleC2×C4×C13C25
hypercenterC2×C4×Q16D13
hypocenterC13C2×#2947
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

2730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033672);