Finite Group Databasebeta

#102×Dic191 #37572337

order24448
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct product#102×Dic191

Splittings

SylowC191 ⋊ C4×#102

Subgroups

subgroupG/H
centerC23D4×D191
commutatorC4×C191C2×C42
FrattiniC22×C4C22×D191
FittingC2×#102×C191C2
socleC23×C191C2×D4
prime radicalC22×D4×C191C22
cosocleC22×C4×C191C23
hypercenterC2×#102D191
hypocenterC191C4×#102
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

2716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 4327);