Finite Group Databasebeta

C2×#22565228 #31027014

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22565228

Splittings

SylowC67 ⋊ C2×#2550

Subgroups

subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC22×#125×C67C2
socle, prime radicalC24×C67C24
hypercenterC22×#125D67
hypocenterC67C2×#2550
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×#125

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

1924 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 340751);