Finite Group Databasebeta

C2×C4×#14581798 #36267805

order21248
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×#14581798

Splittings

FittingC22×C4×C8×C83 ⋊ C2
SylowC83 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC2×C4×C8C2×D83
commutatorC2×C83C23×C42
FrattiniC2×C4C24×D83
FittingC22×C4×C8×C83C2
socleC23×C83C23×C4
prime radicalC22×#13050590C22
cosocleC2×C4×C83C25
hypercenterC22×C4×C8D83
hypocenterC83C2×C4×#131
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4×C8 ◁ C22×C4×C8

3366 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, 1032969);