Finite Group Databasebeta

#14565401

order2432
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

SylowC19 ⋊ #2153

Subgroups

subgroupG/H
centerC8C2×D76
commutatorC4×C19C22×C8
FrattiniC2×C8C22×D19
FittingC19×#405C2
socleC2×C19C2×C4⋊C8
prime radicalC23×C19M16
cosocleC2×C8×C19C23
hypercenter#405D19
hypocenterC19#2153
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C8 ◁ C22×C8 ◁ #405

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Polycyclic presentation:

2^7,19|a^2=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^18,c^b=cg

Conjugacy classes & character table

404 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6276);