Finite Group Databasebeta

#37581464

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

Aliases

No aliases for this group.

Splittings

SylowC191 ⋊ #2962

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D191
commutator, socleC22×C191C23×C4
Fitting#405×C191C2
prime radicalC23×C191C22×C4
cosocleC2×C4×C191C24
hypercenter#405D191
hypocenterC191#2962
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ #405

356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Polycyclic presentation:

2^7,191|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,h^b=h^190,d^c=dg

Conjugacy classes & character table

3850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 13454);