Finite Group Databasebeta

C22×#11745664 #16838162

order3776
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11745664

Splittings

SylowC59 ⋊ C22×M16

Subgroups

subgroupG/H
centerC22×C4C2×D59
commutatorC2×C59C23×C4
FrattiniC4C23×D59
FittingC23×C4×C59C2
socleC23×C59C2×C4
prime radicalC24×C59C4
cosocleC4×C59C24
hypercenterC23×C4D59
hypocenterC59C22×M16
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C23×C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 1309);