Finite Group Databasebeta

C2×#24911750 #35574223

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#24911750

Splittings

SylowC83 ⋊ C2×#2484

Subgroups

subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC23×C4⋊C4×C83C2
socleC24×C83C24
prime radicalC25×C83C23
hypercenterC23×C4⋊C4D83
hypocenterC83C2×#2484
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C23×C4⋊C4

2918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 339387);