Finite Group Databasebeta

C2×#22562149 #31009600

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

Aliases

direct productC2×#22562149

Splittings

SylowC67 ⋊ C2×#2189

Subgroups

subgroupG/H
centerC23C2×#11761613
commutator, cosocleC2×C8×C67C24
FrattiniC2×C8C23×D67
Fitting, prime radicalC22×#135×C67C2
socleC23×C67C2×D8
hypercenterC22×#135D67
hypocenterC67C2×#2189
LCSG ▷ C2×C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#135

1146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1906 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 323337);