Finite Group Databasebeta

C2×#22561381 #30883255

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22561381

Splittings

SylowC67 ⋊ C2×#2031

Subgroups

subgroupG/H
centerC2×C4#14524029
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC22×#104×C67C2
socleC22×C67#393
prime radicalC22×#41×C67C22
hypercenterC22×#104D67
hypocenterC67C2×#2031
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

1234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 196992);