Finite Group Databasebeta

C2×#22569221 #31720324

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

Aliases

direct productC2×#22569221

Splittings

FittingC2×#432×C67 ⋊ C2
SylowC67 ⋊ C2×#2970

Subgroups

subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×#432×C67C2
socleC23×C67C23×C4
prime radicalC22×#11761628C4
cosocleC2×C4×C67C25
hypercenterC2×#432D67
hypocenterC67C2×#2970
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×#432

2254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1948 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1034061);