Finite Group Databasebeta

C22×#22604395 #49148396

order36928
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#22604395

Splittings

FittingC23×C4×C577 ⋊ C2
SylowC577 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D577
commutatorC2×C577C23×C4
FrattiniC22C23×D577
FittingC23×C4×C577C2
socleC24×C577C22
prime radicalC24×D577C2
cosocleC22×C577C24
hypercenterC23×C4D577
hypocenterC577C22×C22⋊C4
LCSG ▷ C2×C577 ▷ C577
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18464

Conjugacy classes & character table

9256 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36928, 996);