Finite Group Databasebeta

C22×#16863703 #31723320

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

Aliases

direct productC22×#16863703

Splittings

SylowC67 ⋊ C22×#479

Subgroups

subgroupG/H
centerC24C2×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC22×C4×Q8×C67C2
socle, prime radicalC24×C67C2×D4
hypercenterC22×C4×Q8D67
hypocenterC67C22×#479
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×Q8

2142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1037057);