Finite Group Databasebeta

C22×#16837183 #28741374

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#16837183

Splittings

FittingC22×M32×C59 ⋊ C2
SylowC59 ⋊ C22×#349

Subgroups

subgroupG/H
centerC22×C4(C2×D59)⋊C4
commutatorC22×C59C23×C8
FrattiniC2×C8C23×D59
FittingC22×M32×C59C2
socleC23×C59C22⋊C8
prime radicalC24×D59C8
cosocleC2×C8×C59C24
hypercenterC22×M32D59
hypocenterC59C22×#349
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×M32

1262 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, 322253);