Finite Group Databasebeta

C2×#14531785 #17193837

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14531785

Splittings

FittingC22×C4×Q8×C17 ⋊ C2
SylowC17 ⋊ C2×#2360

Subgroups

subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC22×C4×Q8×C17C2
socleC24×C17C24
prime radicalC24×D17C23
cosocleC23×C17C25
hypercenterC22×C4×Q8D17
hypocenterC17C2×#2360
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×Q8

3614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 329081);