Finite Group Databasebeta

C2×#14526658 #16924267

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14526658

Splittings

SylowC17 ⋊ C2×#1292

Subgroups

subgroupG/H
centerC23#10587502
commutatorC2×C4×C17C2×C42
FrattiniC2×C42C22×D17
FittingC2×C17×#423C2
socleC23×C17#95
prime radicalC24×C17C4⋊C4
cosocleC2×C42×C17C23
hypercenterC2×#423D17
hypocenterC17C2×#1292
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 59511);