Finite Group Databasebeta

C22×#16837737 #29456447

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC22×#16837737

Splittings

SylowC59 ⋊ C22×#484

Subgroups

subgroupG/H
centerC24C2×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC23×C4⋊C4×C59C2
socleC24×C59C2×D4
prime radicalC25×C59D4
hypercenterC23×C4⋊C4D59
hypocenterC59C22×#484
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×C4⋊C4

2662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1037326);