Finite Group Databasebeta

#41×Dic43 #14583370

order2752
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#41×Dic43

Splittings

SylowC43 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D43
commutatorC2×C43C23×C4
FrattiniC22C23×D43
Fitting, prime radicalC2×#41×C43C2
socle, cosocleC22×C43C24
hypercenterC2×#41D43
hypocenterC43C4×#41
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×#41

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1376

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 1020);