Finite Group Databasebeta

C23×C4×Dic34 #17940893

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

Aliases

direct productC23×C4×Dic34

Splittings

SylowC17 ⋊ C23×C4×Q8

Subgroups

subgroupG/H
centerC24×C4C2×D17
commutatorC2×C17C25×C4
FrattiniC22C25×D17
FittingC23×C42×C17C2
socle, prime radicalC25×C17C23
cosocleC22×C17C26
hypercenterC23×C42D17
hypocenterC17C23×C4×Q8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C24×C4 ◁ C23×C42

12446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

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, 1076137);