Finite Group Databasebeta

#41×Dic367 #37554657

order23488
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#41×Dic367

Splittings

SylowC367 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D367
commutatorC2×C367C23×C4
FrattiniC22C23×D367
Fitting, prime radicalC2×#41×C367C2
socle, cosocleC22×C367C24
hypercenterC2×#41D367
hypocenterC367C4×#41
LCSG ▷ C2×C367 ▷ C367
UCSC1 ◁ C2×C4 ◁ C2×#41

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

3700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 1020);