Finite Group Databasebeta

C2×#13130010 #16791516

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13130010

Splittings

FittingC24×C4×C13 ⋊ C4
SylowC13 ⋊ C2×C22⋊#95

Subgroups

subgroupG/H
centerC24C22×#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC24×C4×C13C4
socleC24×C13C22×C4
prime radicalC25×D13C22
cosocleC23×D13C24
hypercenterC24×C4#261
hypocenterC13C2×C22⋊#95
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4

7630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1098165);