Finite Group Databasebeta

#41×C22⋊Dic59 #28747894

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

Aliases

direct product#41×C22⋊Dic59

Splittings

SylowC59 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
Fitting, prime radicalC23×#41×C59C2
socle, cosocleC23×C59C25
hypercenterC23×#41D59
hypocenterC59C22⋊C4×#41
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C23×#41

5646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 328773);