Finite Group Databasebeta

C2×#14537894 #17899370

order4352
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14537894

Splittings

FittingC2×C8×Q8×C17 ⋊ C2
SylowC17 ⋊ C2×#2988

Subgroups

subgroupG/H
centerC22×C4C23×D17
commutatorC2×C17C24×C8
FrattiniC2×C4C24×D17
FittingC2×C8×Q8×C17C2
socleC23×C17C23×C4
prime radicalC22×#63256C4
cosocleC2×C4×C17C25
hypercenterC2×C8×Q8D17
hypocenterC17C2×#2988
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

2434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 1034614);