Finite Group Databasebeta

#44469993

order29888
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #405

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D467
commutatorC2×C467C2×C42
Fitting#117×C467C2
socleC22×C467C22×C4
prime radicalC23×C467C2×C4
cosocleC2×C4×C467C23
hypercenter#117D467
hypocenterC467#405
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C2×C4 ◁ #117

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Polycyclic presentation:

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

Conjugacy classes & character table

4700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 505);