Finite Group Databasebeta

#41×Dic523 #45690676

order33472
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#41×Dic523

Splittings

SylowC523 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D523
commutatorC2×C523C23×C4
FrattiniC22C23×D523
Fitting, prime radicalC2×#41×C523C2
socle, cosocleC22×C523C24
hypercenterC2×#41D523
hypocenterC523C4×#41
LCSG ▷ C2×C523 ▷ C523
UCSC1 ◁ C2×C4 ◁ C2×#41

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16736

Conjugacy classes & character table

5260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 1020);