Finite Group Databasebeta

#44469857

order29888
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #364

Subgroups

subgroupG/H
centerC8C22⋊D467
commutatorC4×C467C2×C8
FrattiniC2×C8C2×D467
FittingM32×C467C2
socleC2×C467C4⋊C8
prime radicalC22×C467M16
cosocleC2×C8×C467C22
hypercenterM32D467
hypocenterC467#364
LCSG ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C8 ◁ C2×C8 ◁ M32

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7472

Polycyclic presentation:

2^6,467|a^2=d,b^2=c,c^2=f,d^2=e,e^2=f,b^a=bc,c^a=cf,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, 369);