Finite Group Databasebeta

C2×#14526619 #16923780

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14526619

Splittings

SylowC17 ⋊ C2×#1277

Subgroups

subgroupG/H
centerC23×C4D68
commutatorC4×C17C2×C4×C8
FrattiniC2×C42C22×D17
FittingC22×C4×C8×C17C2
socle, prime radicalC24×C17C4⋊C4
cosocleC2×C42×C17C23
hypercenterC22×C4×C8D17
hypocenterC17C2×#1277
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

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, 59024);