Finite Group Databasebeta

C22×#16863177 #31008516

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#16863177

Splittings

FittingC22×M32×C67 ⋊ C2
SylowC67 ⋊ C22×#349

Subgroups

subgroupG/H
centerC22×C4(C2×D67)⋊C4
commutatorC22×C67C23×C8
FrattiniC2×C8C23×D67
FittingC22×M32×C67C2
socleC23×C67C22⋊C8
prime radicalC24×D67C8
cosocleC2×C8×C67C24
hypercenterC22×M32D67
hypocenterC67C22×#349
LCSG ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×M32

1262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

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, 322253);