Finite Group Databasebeta

C23×Dic734 #37555010

order23488
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×Dic734

Splittings

SylowC367 ⋊ C23×Q8

Subgroups

subgroupG/H
centerC24C2×D367
commutator, cosocleC2×C367C25
FrattiniC2C24×D367
FittingC23×C4×C367C2
socle, prime radicalC24×C367C22
hypercenterC23×C4D367
hypocenterC367C23×Q8
LCSG ▷ C2×C367 ▷ C367
UCSC1 ◁ C24 ◁ C23×C4

850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23488

Conjugacy classes & character table

5896 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 1373);