Finite Group Databasebeta

#427×D191 #37581096

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct product#427×D191

Splittings

Fitting#427×C191 ⋊ C2
SylowC191 ⋊ C2×#427

Subgroups

subgroupG/H
centerC2×C4D4×D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
Fitting#427×C191C2
socleC22×C191C22×D4
prime radicalC23×D191D4
cosocleC2×C4×C191C24
hypercenter#427D191
hypocenterC191C2×#427
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6112

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, 13086);