Finite Group Databasebeta

C22×#22550838 #45655685

order32576
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#22550838

Splittings

FittingC23×C4×C509 ⋊ C2
SylowC509 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D509
commutatorC2×C509C23×C4
FrattiniC22C23×D509
FittingC23×C4×C509C2
socleC24×C509C22
prime radicalC24×D509C2
cosocleC22×C509C24
hypercenterC23×C4D509
hypocenterC509C22×C22⋊C4
LCSG ▷ C2×C509 ▷ C509
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16288

Conjugacy classes & character table

8168 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32576, 996);