Finite Group Databasebeta

C2×#14531149 #17192548

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#14531149

Splittings

SylowC17 ⋊ C2×#2276

Subgroups

subgroupG/H
centerC24C23×D17
commutatorC2×C17C23×C42
FrattiniC23C24×D17
FittingC22×C4×Q8×C17C2
socle, prime radicalC24×C17C24
cosocleC23×C17C25
hypercenterC22×C4×Q8D17
hypocenterC17C2×#2276
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×Q8

3654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327792);