Finite Group Databasebeta

C22×#19127920 #36271209

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#19127920

Splittings

SylowC83 ⋊ C22×#464

Subgroups

subgroupG/H
centerC24C2×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC22×#124×C83C2
socleC24×C83C2×D4
prime radicalC23×D4×C83C22
hypercenterC22×#124D83
hypocenterC83C22×#464
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#124

2918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

2372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1036373);