Finite Group Databasebeta

#99×Dic118 #28605237

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#99×Dic118

Splittings

SylowC59 ⋊ Q8×#99

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC4×#99×C59C2
socleC22×C59C22×C22⋊C4
prime radicalC22×D4×C59C23
cosocleC24×C59C24
hypercenterC4×#99D59
hypocenterC59Q8×#99
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

1354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1331 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 186116);