Finite Group Databasebeta

C2×#13117801 #16022286

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#13117801

Splittings

SylowC13 ⋊ C2×#2356

Subgroups

subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC22×C4×Q8×C13C2
socle, prime radicalC24×C13C24
cosocleC23×C13C25
hypercenterC22×C4×Q8D13
hypocenterC13C2×#2356
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×Q8

2550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 328935);