Finite Group Databasebeta

C23×#14273642 #29452150

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×#14273642

Splittings

SylowC59 ⋊ C23×#99

Subgroups

subgroupG/H
centerC24C22⋊Dic59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
Fitting, prime radicalC24×D4×C59C2
socleC24×C59C22⋊C4
cosocleC23×C59C25
hypercenterC24×D4D59
hypocenterC59C23×#99
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C26 ◁ C24×D4

7902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033029);