Finite Group Databasebeta

C23×#14273707 #29495333

order15104
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC23×#14273707

Splittings

FittingC23×C4⋊C4×C59 ⋊ C2
SylowC59 ⋊ C23×C22⋊Q8

Subgroups

subgroupG/H
centerC25C22×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC23×C4⋊C4×C59C2
socleC25×C59C23
prime radicalC25×D59C22
hypercenterC23×C4⋊C4D59
hypocenterC59C23×C22⋊Q8
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C25 ◁ C23×C4⋊C4

14078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076212);