Finite Group Databasebeta

C22×#16863640 #31722942

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

Aliases

direct productC22×#16863640

Splittings

SylowC67 ⋊ C22×#468

Subgroups

subgroupG/H
centerC24C2×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
Fitting, prime radicalC22×#121×C67C2
socleC24×C67C2×D4
hypercenterC22×#121D67
hypocenterC67C22×#468
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#121

3222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1036679);