Finite Group Databasebeta

C23×#88058 #16726564

order3328
isoclinismisoclinic class of #6095
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#88058

Splittings

SylowC13 ⋊ C23×#107

Subgroups

subgroupG/H
centerC25D52
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC24×C8×C13C2
socle, prime radicalC25×C13D4
cosocleC2×C4×C13C25
hypercenterC24×C8D13
hypocenterC13C23×#107
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×C4 ◁ C24×C8

3614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033213);