Finite Group Databasebeta

C22×#16837675 #29456074

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

Aliases

direct productC22×#16837675

Splittings

SylowC59 ⋊ C22×#473

Subgroups

subgroupG/H
centerC23#14273699
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×#137×C59C2
socleC23×C59#121
prime radicalC22×#41×C59C22
hypercenterC22×#137D59
hypocenterC59C22×#473
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

2630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1036953);