Finite Group Databasebeta

C4×#19127624 #35326262

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#19127624

Splittings

SylowC83 ⋊ C4×#396

Subgroups

subgroupG/H
centerC23×C4C22×D83
commutatorC23×C83C23×C4
FrattiniC24C23×D83
FittingC2×C4×C22⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×C4×C22⋊C4D83
hypocenterC83C4×#396
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

1966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 91426);