Finite Group Databasebeta

C8×C22⋊#1057 #16780315

order3328
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C23×C8

Aliases

direct productC8×C22⋊#1057

Splittings

SylowC13 ⋊ C8×C22⋊C8

Subgroups

subgroupG/H
centerC22×C8C2×#261
commutatorC2×C13C2×C82
FrattiniC22×C4C22×#261
FittingC23×C8×C13C4
socleC23×C13C2×C42
prime radicalC24×C13C42
cosocleC2×C4×Dic13C23
hypercenterC23×C8#261
hypocenterC13C8×C22⋊C8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C23×C8

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1086964);