Finite Group Databasebeta

C23×C22⋊#3622 #17897751

order4352
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC23×C22⋊#3622

Splittings

SylowC17 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC24×C4C2×D17
commutatorC2×C17C24×C8
FrattiniC2×C4C24×D17
FittingC25×C4×C17C2
socleC25×C17C2×C4
prime radicalC26×C17C4
cosocleC2×C4×C17C25
hypercenterC25×C4D17
hypocenterC17C23×C22⋊C8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C24×C4 ◁ C25×C4

7646 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, 1032995);