Finite Group Databasebeta

C2×#14529588 #17037947

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#14529588

Splittings

FittingC22×C17×#102 ⋊ C2
SylowC17 ⋊ C2×#1957

Subgroups

subgroupG/H
centerC24D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC22×C17×#102C2
socleC24×C17C2×D4
prime radicalC22×#10587626C2
cosocleC22×C4×C17C24
hypercenterC22×#102D17
hypocenterC17C2×#1957
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

2414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 173191);