Finite Group Databasebeta

C22×C8×D68 #17898157

order4352
isoclinismisoclinic class of Dic34
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×C8×D68

Splittings

FittingC22×C4×C8×C17 ⋊ C2
SylowC17 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC23×C8C2×D17
commutatorC2×C17C24×C8
FrattiniC2×C4C24×D17
FittingC22×C4×C8×C17C2
socleC24×C17C22×C4
prime radicalC23×D68C4
cosocleC2×C4×C17C25
hypercenterC22×C4×C8D17
hypocenterC17C22×C8×D4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

3694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033401);