Finite Group Databasebeta

C2×#22570970 #31726361

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

Aliases

direct productC2×#22570970

Splittings

FittingC2×#525×C67 ⋊ C2
SylowC67 ⋊ C2×#3188

Subgroups

subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#525×C67C2
socleC23×C67C22×D4
hypercenterC2×#525D67
hypocenterC67C2×#3188
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

2718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1040098);