Finite Group Databasebeta

C22×#16863513 #31720122

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

Aliases

direct productC22×#16863513

Splittings

SylowC67 ⋊ C22×#443

Subgroups

subgroupG/H
centerC22×C4D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
Fitting, prime radicalC22×#135×C67C2
socleC23×C67C4×D4
cosocleC2×C4×C67C25
hypercenterC22×#135D67
hypocenterC67C22×#443
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#135

2750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

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, 1033859);