Finite Group Databasebeta

C2×#22562414 #31010606

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

Aliases

direct productC2×#22562414

Splittings

SylowC67 ⋊ C2×#2237

Subgroups

subgroupG/H
centerC23C2×#11761613
commutator, cosocleC2×C8×C67C24
FrattiniC2×C8C23×D67
FittingC2×#467×C67C2
socleC23×C67C2×D8
prime radicalC24×C67D8
hypercenterC2×#467D67
hypocenterC67C2×#2237
LCSG ▷ C2×C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 324343);