Finite Group Databasebeta

C23×#14273684 #29495247

order15104
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4

Aliases

direct productC23×#14273684

Splittings

FittingC23×C42×C59 ⋊ C2
SylowC59 ⋊ C23×#117

Subgroups

subgroupG/H
centerC24×C4C2×D59
commutatorC2×C59C25×C4
FrattiniC22C25×D59
FittingC23×C42×C59C2
socleC25×C59C23
prime radicalC25×D59C22
cosocleC22×C59C26
hypercenterC23×C42D59
hypocenterC59C23×#117
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C24×C4 ◁ C23×C42

14334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076126);