Finite Group Databasebeta

#367×D191 #37574298

order24448
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#367×D191

Splittings

Fitting#367×C191 ⋊ C2
SylowC191 ⋊ C2×#367

Subgroups

subgroupG/H
centerC22D8×D191
commutatorC8×C191C22×C4
FrattiniC2×C8C22×D191
Fitting#367×C191C2
socleC22×C191C2×D8
prime radicalC22×D191D8
cosocleC2×C8×C191C23
hypercenter#367D191
hypocenterC191C2×#367
LCSG ▷ C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

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, 6288);