Finite Group Databasebeta

#99×#1055 #15753462

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct product#99×#1055

Splittings

SylowC13 ⋊ C8×#99

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC22×C13C2×C4×C8
FrattiniC23×C4C22×D13
FittingC4×C13×#99C2
socleC22×C13C4×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC23×C4×C13C23
hypercenterC4×#99D13
hypocenterC13C8×#99
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 60111);