Finite Group Databasebeta

C22×C4×#63252 #17940898

order4352
isoclinismisoclinic class of Dic34
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×C4×#63252

Splittings

FittingC23×C42×C17 ⋊ C2
SylowC17 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC22×C42C2×D17
commutatorC2×C17C25×C4
FrattiniC22C25×D17
FittingC23×C42×C17C2
socleC24×C17C24
prime radicalC23×#63252C2
cosocleC22×C17C26
hypercenterC23×C42D17
hypocenterC17C22×C4×#41
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C42 ◁ C23×C42

12878 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, 1076142);