Finite Group Databasebeta

#99×C59⋊C8 #28479232

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct product#99×C59⋊C8

Splittings

SylowC59 ⋊ C8×#99

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D59
commutatorC22×C59C2×C4×C8
FrattiniC23×C4C22×D59
FittingC4×#99×C59C2
socleC22×C59C4×C22⋊C4
prime radicalC22×D4×C59C2×C4
cosocleC23×C4×C59C23
hypercenterC4×#99D59
hypocenterC59C8×#99
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 60111);