Finite Group Databasebeta

C4×(C2×#261)⋊C8 #16785172

order3328
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×(C2×#261)⋊C8

Splittings

FittingC2×C4×C8×C13 ⋊ C4
SylowC13 ⋊ C4×#336

Subgroups

subgroupG/H
centerC2×C42C2×#261
commutatorC2×C13C42×C8
FrattiniC22×C4C22×#261
FittingC2×C4×C8×C13C4
socleC23×C13C2×C42
prime radicalC23×D13C22×C4
cosocleC22×C4×D13C23
hypercenterC2×C4×C8#261
hypocenterC13C4×#336
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

1318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1091821);