Finite Group Databasebeta

#430×D191 #37581124

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

Aliases

direct product#430×D191

Splittings

Fitting#430×C191 ⋊ C2
SylowC191 ⋊ C2×#430

Subgroups

subgroupG/H
centerC4C2×D4×D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
Fitting#430×C191C2
socleC2×C191C22×C4⋊C4
prime radicalC23×D191Q8
cosocleC2×C4×C191C24
hypercenter#430D191
hypocenterC191C2×#430
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C4 ◁ C22×C4 ◁ #430

460 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, 13114);