Finite Group Databasebeta

C2×#14531077 #17192432

order4352
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14531077

Splittings

FittingC22×C17×C32 ⋊ C2
SylowC17 ⋊ C2×#2258

Subgroups

subgroupG/H
centerC2×C32C2×D17
commutatorC2×C17C23×C16
FrattiniC16C23×D17
FittingC22×C17×C32C2
socleC22×C17C22×C16
prime radicalC2×#63252C8
cosocleC16×C17C24
hypercenterC22×C32D17
hypocenterC17C2×#2258
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C32 ◁ C22×C32

470 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, 327676);