Finite Group Databasebeta

C2×#13117791 #16022275

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

Aliases

direct productC2×#13117791

Splittings

SylowC13 ⋊ C2×#2355

Subgroups

subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C4×C13×C4⋊C4C2
socle, prime radicalC24×C13C24
cosocleC23×C13C25
hypercenterC2×C4×C4⋊C4D13
hypocenterC13C2×#2355
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

2638 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, 328924);