Finite Group Databasebeta

#41×Dic463 #44445264

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

Aliases

direct product#41×Dic463

Splittings

SylowC463 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D463
commutatorC2×C463C23×C4
FrattiniC22C23×D463
Fitting, prime radicalC2×#41×C463C2
socle, cosocleC22×C463C24
hypercenterC2×#41D463
hypocenterC463C4×#41
LCSG ▷ C2×C463 ▷ C463
UCSC1 ◁ C2×C4 ◁ C2×#41

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14816

Conjugacy classes & character table

4660 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29632, 1020);