Finite Group Databasebeta

C22×#16837156 #28586039

order15104
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C28

Aliases

direct productC22×#16837156

Splittings

SylowC59 ⋊ C22×#336

Subgroups

subgroupG/H
centerC24×C4C2×D59
commutatorC2×C59C22×C4×C8
FrattiniC22×C4C23×D59
FittingC24×C8×C59C2
socle, prime radicalC25×C59C2×C4
cosocleC22×C4×C59C24
hypercenterC24×C8D59
hypocenterC59C22×#336
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C24×C4 ◁ C24×C8

3086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 166918);