Finite Group Databasebeta

C2×#22561640 #30884667

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

Aliases

direct productC2×#22561640

Splittings

SylowC67 ⋊ C2×#2076

Subgroups

subgroupG/H
centerC24C2×C22⋊D67
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC2×#380×C67C2
socleC24×C67C2×D4
prime radicalC25×C67D4
hypercenterC2×#380D67
hypocenterC67C2×#2076
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

1270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 198404);