Finite Group Databasebeta

C22×#16837125 #28554474

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#16837125

Splittings

FittingC22×C22⋊C8×C59 ⋊ C2
SylowC59 ⋊ C22×#323

Subgroups

subgroupG/H
centerC24(C2×D59)⋊C4
commutatorC22×C59C23×C8
FrattiniC22×C4C23×D59
FittingC22×C22⋊C8×C59C2
socleC24×C59C22⋊C4
prime radicalC25×D59C4
cosocleC22×C4×C59C24
hypercenterC22×C22⋊C8D59
hypocenterC59C22×#323
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

2878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 135353);