Finite Group Databasebeta

C22×#11745671 #16838174

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

Aliases

direct productC22×#11745671

Splittings

FittingC22×Q8×C59 ⋊ C2
SylowC59 ⋊ C22×SD16

Subgroups

subgroupG/H
centerC23C22⋊D59
commutator, cosocleC4×C59C24
FrattiniC4C23×D59
FittingC22×Q8×C59C2
socleC23×C59D4
prime radicalC22×D236C2
hypercenterC22×Q8D59
hypocenterC59C22×SD16
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 1321);