Finite Group Databasebeta

#44445276

order29632
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

SylowC463 ⋊ #520

Subgroups

subgroupG/H
center, FrattiniC22C23×D463
commutatorC2×C463C23×C4
Fitting, prime radicalC2×#41×C463C2
socle, cosocleC22×C463C24
hypercenterC2×#41D463
hypocenterC463#520
LCSG ▷ C2×C463 ▷ C463
UCSC1 ◁ C22 ◁ C2×#41

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14816

Polycyclic presentation:

2^6,463|a^2=f,d^2=e,b^a=be,d^a=de,g^a=g^462,c^b=ce

Conjugacy classes & character table

4654 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29632, 1032);