Finite Group Databasebeta

C2×#14544576 #17968523

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14544576

Splittings

SylowC17 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC2×C17C22×C4×C8
FrattiniC23C23×#595
FittingC2×C17×#95C4
socle, prime radicalC24×C17C22×C4
cosocleC22×Dic17C24
hypercenterC2×#95#595
hypocenterC17C2×C8×C4⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#95

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103767);