Finite Group Databasebeta

#44469779

order29888
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #330

Subgroups

subgroupG/H
centerC22C22⋊Dic467
commutatorC2×C4×C467C2×C4
FrattiniC42C2×D467
Fitting#125×C467C2
socle, prime radicalC22×C467C22⋊C4
cosocleC42×C467C22
hypercenter#125D467
hypocenterC467#330
LCSG ▷ C2×C4×C467 ▷ C22×C467 ▷ C467
UCSC1 ◁ C22 ◁ C42 ◁ #125

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29888

Polycyclic presentation:

2^6,467|a^2=d,b^2=e,c^2=f,d^2=e,b^a=bc,c^a=ce,g^a=g^466,c^b=cf,d^b=def

Conjugacy classes & character table

3281 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 291);