Finite Group Databasebeta

C2×#24907291 #35402164

order21248
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#24907291

Splittings

FittingC2×C4×C4⋊C4×C83 ⋊ C2
SylowC83 ⋊ C2×#1762

Subgroups

subgroupG/H
centerC24C2×C22⋊D83
commutatorC4×C83C22×C42
FrattiniC22×C4C23×D83
FittingC2×C4×C4⋊C4×C83C2
socleC24×C83C2×D4
prime radicalC23×D332C22
cosocleC22×C4×C83C24
hypercenterC2×C4×C4⋊C4D83
hypocenterC83C2×#1762
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×C4×C4⋊C4

2118 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, 167328);