Finite Group Databasebeta

#423×D191 #37581072

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#423×D191

Splittings

Fitting#423×C191 ⋊ C2
SylowC191 ⋊ C2×#423

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D191
commutator, socleC22×C191C23×C4
Fitting#423×C191C2
prime radicalC23×D191C2×C4
cosocleC2×C4×C191C24
hypercenter#423D191
hypocenterC191C2×#423
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ #423

576 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, 13062);