Finite Group Databasebeta

C23×#14273654 #29452277

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#14273654

Splittings

SylowC59 ⋊ C23×#104

Subgroups

subgroupG/H
centerC23×C4C22⋊D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
Fitting, prime radicalC23×#41×C59C2
socleC24×C59C22⋊C4
cosocleC2×C4×C59C25
hypercenterC23×#41D59
hypocenterC59C23×#104
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C23×#41

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 1033156);