Finite Group Databasebeta

C22×#11745672 #16838178

order3776
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11745672

Splittings

SylowC59 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23C22⋊D59
commutator, cosocleC4×C59C24
FrattiniC4C23×D59
FittingC22×Q8×C59C2
socle, prime radicalC23×C59D4
hypercenterC22×Q8D59
hypocenterC59C22×Q16
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 1325);