Finite Group Databasebeta

C2×#22562246 #31010072

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

Aliases

direct productC2×#22562246

Splittings

SylowC67 ⋊ C2×#2207

Subgroups

subgroupG/H
centerC23C2×#11761613
commutator, cosocleC2×C8×C67C24
FrattiniC2×C8C23×D67
Fitting, prime radicalC2×#493×C67C2
socleC23×C67C2×D8
hypercenterC2×#493D67
hypocenterC67C2×#2207
LCSG ▷ C2×C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#493

806 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, 323809);