Finite Group Databasebeta

C2×#22562688 #31014209

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22562688

Splittings

SylowC67 ⋊ C2×#2296

Subgroups

subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#385×C67C2
socleC24×C67C24
prime radicalC25×C67C23
cosocleC23×C67C25
hypercenterC2×#385D67
hypocenterC67C2×#2296
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#385

3854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 327946);