Finite Group Databasebeta

C22×#16863669 #31723216

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#16863669

Splittings

SylowC67 ⋊ C22×#473

Subgroups

subgroupG/H
centerC23#14524015
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC22×#137×C67C2
socleC23×C67#121
prime radicalC22×#41×C67C22
hypercenterC22×#137D67
hypocenterC67C22×#473
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

2630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1516 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1036953);