Finite Group Databasebeta

C2×#14527043 #16956013

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14527043

Splittings

SylowC17 ⋊ C2×#1442

Subgroups

subgroupG/H
centerC25C22×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC23×C4⋊C4×C17C2
socle, prime radicalC25×C17C23
cosocleC24×C17C24
hypercenterC23×C4⋊C4D17
hypocenterC17C2×#1442
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C25 ◁ C23×C4⋊C4

2942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 91257);