Finite Group Databasebeta

C2×#14527014 #16955429

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#14527014

Splittings

SylowC17 ⋊ C2×C4⋊#95

Subgroups

subgroupG/H
centerC25C22×D17
commutatorC22×C17C22×C42
FrattiniC24C23×D17
FittingC23×C42×C17C2
socle, prime radicalC25×C17C23
cosocleC24×C17C24
hypercenterC23×C42D17
hypocenterC17C2×C4⋊#95
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C25 ◁ C23×C42

3854 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, 90673);