Finite Group Databasebeta

C22×#16863392 #31719349

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#16863392

Splittings

SylowC67 ⋊ C22×#416

Subgroups

subgroupG/H
centerC23×C4C22⋊D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
Fitting, prime radicalC23×#41×C67C2
socleC24×C67C2×D4
cosocleC2×C4×C67C25
hypercenterC23×#41D67
hypocenterC67C22×#416
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C23×#41

5326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2752 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033086);