Finite Group Databasebeta

C2×#22568742 #31719389

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#22568742

Splittings

SylowC67 ⋊ C2×#2898

Subgroups

subgroupG/H
centerC23C22×C22⋊D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
Fitting, prime radicalC22×2−1+4×C67C2
socleC23×C67C22×D4
cosocleC2×C4×C67C25
hypercenterC22×2−1+4D67
hypocenterC67C2×#2898
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×2−1+4

4882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2332 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033126);