Finite Group Databasebeta

C2×#22561666 #30884765

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22561666

Splittings

SylowC67 ⋊ C2×#2081

Subgroups

subgroupG/H
centerC22#16863321
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC2×#418×C67C2
socleC22×C67#397
prime radicalC23×D4×C67C22
hypercenterC2×#418D67
hypocenterC67C2×#2081
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#418

1006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1498 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 198502);