Finite Group Databasebeta

C23×#14581749 #36310962

order21248
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4

Aliases

direct productC23×#14581749

Splittings

FittingC23×C42×C83 ⋊ C2
SylowC83 ⋊ C23×#117

Subgroups

subgroupG/H
centerC24×C4C2×D83
commutatorC2×C83C25×C4
FrattiniC22C25×D83
FittingC23×C42×C83C2
socleC25×C83C23
prime radicalC25×D83C22
cosocleC22×C83C26
hypercenterC23×C42D83
hypocenterC83C23×#117
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C24×C4 ◁ C23×C42

14334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

5408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1076126);