Finite Group Databasebeta

C2×#14530617 #17187489

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14530617

Splittings

FittingC2×C4×C16×C17 ⋊ C2
SylowC17 ⋊ C2×#2169

Subgroups

subgroupG/H
centerC22×C8C22×D17
commutatorC22×C17C23×C8
FrattiniC2×C8C23×D17
FittingC2×C4×C16×C17C2
socleC23×C17C22×C8
prime radicalC22×D68C8
cosocleC2×C8×C17C24
hypercenterC2×C4×C16D17
hypocenterC17C2×#2169
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C2×C4×C16

742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322733);