Finite Group Databasebeta

C2×#22565215 #31025875

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22565215

Splittings

SylowC67 ⋊ C2×#2549

Subgroups

subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×C4×C22⋊C4×C67C2
socleC24×C67C24
prime radicalC25×C67C23
hypercenterC2×C4×C22⋊C4D67
hypocenterC67C2×#2549
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

3094 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 339612);