Finite Group Databasebeta

C2×C4×#14581712 #35402145

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

Aliases

direct productC2×C4×#14581712

Splittings

FittingC2×C4×C4⋊C4×C83 ⋊ C2
SylowC83 ⋊ C2×C4×#102

Subgroups

subgroupG/H
centerC23×C4C22⋊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×C4×#102
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

2158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3392 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 167309);