Finite Group Databasebeta

C22×#41×Dic59 #29495265

order15104
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×#41×Dic59

Splittings

SylowC59 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutatorC2×C59C25×C4
FrattiniC22C25×D59
Fitting, prime radicalC23×#41×C59C2
socleC24×C59C24
cosocleC22×C59C26
hypercenterC23×#41D59
hypocenterC59C22×C4×#41
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C23×#41

12878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076144);