Finite Group Databasebeta

C2×C4×C8×#261 #16796715

order3328
isoclinismisoclinic class of #261
automorphism?
homologyAbelianization (H1) = C2×C42×C8 · Schur multiplier (H2) = C23×C43

Aliases

direct productC2×C4×C8×#261

Splittings

FittingC2×C4×C8×C13 ⋊ C4
derived, SylowC13 ⋊ C2×C42×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C8#261
commutator, hypocenterC13C2×C42×C8
FrattiniC2×C4C23×#261
FittingC2×C4×C8×C13C4
socleC23×C13C2×C42
prime radicalC23×D13C22×C4
cosocleC2×C4×D13C24
LCSG ▷ C13
UCSC1 ◁ C2×C4×C8

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103364);