Finite Group Databasebeta

C22×#16837609 #29455488

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#16837609

Splittings

SylowC59 ⋊ C22×#462

Subgroups

subgroupG/H
centerC24C2×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×C4⋊Q8×C59C2
socle, prime radicalC24×C59C2×D4
hypercenterC22×C4⋊Q8D59
hypocenterC59C22×#462
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊Q8

2790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1036367);