Finite Group Databasebeta

#37570462

order24448
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC191 ⋊ #1323

Subgroups

subgroupG/H
centerC2×C4C22⋊Dic191
commutatorC2×C4×C191C2×C8
FrattiniC22×C8C2×D191
Fitting#424×C191C2
socleC22×C191C22⋊C8
prime radicalC23×C191M16
cosocleC22×C8×C191C22
hypercenter#424D191
hypocenterC191#1323
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Polycyclic presentation:

2^7,191|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^190,c^b=cg,d^b=deg

Conjugacy classes & character table

2698 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 2452);