Finite Group Databasebeta

C2×#22569143 #31720196

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22569143

Splittings

SylowC67 ⋊ C2×#2960

Subgroups

subgroupG/H
centerC22×C8C22×D67
commutatorC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC22×C4×C8×C67C2
socleC23×C67C23×C4
prime radicalC24×C67C22×C4
cosocleC2×C4×C67C25
hypercenterC22×C4×C8D67
hypocenterC67C2×#2960
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C8 ◁ C22×C4×C8

1982 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

4336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033933);