Finite Group Databasebeta

C22×#23748710 #49183162

order37952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#23748710

Splittings

FittingC23×C4×C593 ⋊ C2
SylowC593 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D593
commutatorC2×C593C23×C4
FrattiniC22C23×D593
FittingC23×C4×C593C2
socleC24×C593C22
prime radicalC24×D593C2
cosocleC22×C593C24
hypercenterC23×C4D593
hypocenterC593C22×C22⋊C4
LCSG ▷ C2×C593 ▷ C593
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18976

Conjugacy classes & character table

9512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37952, 996);