Finite Group Databasebeta

C2×#13117748 #16022218

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

Aliases

direct productC2×#13117748

Splittings

SylowC13 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#384C2
socle, prime radicalC24×C13C24
cosocleC23×C13C25
hypercenterC2×#384D13
hypocenterC13C2×Q8×C4⋊C4
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#384

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 328867);