Finite Group Databasebeta

#44470073

order29888
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #427

Subgroups

subgroupG/H
centerC2×C4C22⋊D467
commutatorC4×C467C22×C4
FrattiniC2×C4C22×D467
Fitting#117×C467C2
socleC22×C467C2×D4
prime radicalC23×C467D4
cosocleC2×C4×C467C23
hypercenter#117D467
hypocenterC467#427
LCSG ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Polycyclic presentation:

2^6,467|a^2=e,b^2=d,c^2=f,d^2=f,b^a=bd,d^a=df,g^b=g^466

Conjugacy classes & character table

4688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 585);