Finite Group Databasebeta

#99×D172 #25111922

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct product#99×D172

Splittings

FittingC4×#99×C43 ⋊ C2
SylowC43 ⋊ D4×#99

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC4×#99×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC2×D4×D172C2
cosocleC24×C43C24
hypercenterC4×#99D43
hypocenterC43D4×#99
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

2102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

979 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 184893);