Finite Group Databasebeta

C2×#99×D191 #37580971

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#99×D191

Splittings

FittingC2×#99×C191 ⋊ C2
SylowC191 ⋊ C22×#99

Subgroups

subgroupG/H
centerC22C22⋊C4×D191
commutatorC22×C191C23×C4
FrattiniC23C23×D191
FittingC2×#99×C191C2
socleC22×C191C2×C22⋊C4
prime radicalC22×D4×D191C2
cosocleC23×C191C24
hypercenterC2×#99D191
hypocenterC191C22×#99
LCSG ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

1112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3056

Conjugacy classes & character table

2134 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 12961);