Finite Group Databasebeta

C2×#22569504 #31722265

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#22569504

Splittings

SylowC67 ⋊ C2×#3011

Subgroups

subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
Fitting, prime radicalC22×2−1+4×C67C2
socleC23×C67C22×D4
hypercenterC22×2−1+4D67
hypocenterC67C2×#3011
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×2−1+4

4718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2308 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1036002);