Finite Group Databasebeta

C2×#22563468 #31022073

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

Aliases

direct productC2×#22563468

Splittings

SylowC67 ⋊ C2×#2395

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC22×C4×D4×C67C2
socleC24×C67C24
prime radicalC23×D4×C67C22
hypercenterC22×C4×D4D67
hypocenterC67C2×#2395
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

3182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 335810);