Finite Group Databasebeta

C4×C4⋊C8×D83 #35402273

order21248
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×C4⋊C8×D83

Splittings

FittingC4×C4⋊C8×C83 ⋊ C2
SylowC83 ⋊ C2×C4×C4⋊C8

Subgroups

subgroupG/H
centerC2×C42C22×D83
commutatorC2×C83C22×C4×C8
FrattiniC22×C4C23×D83
FittingC4×C4⋊C8×C83C2
socleC23×C83C23×C4
prime radicalC23×D83C22×C4
cosocleC22×C4×C83C24
hypercenterC4×C4⋊C8D83
hypocenterC83C2×C4×C4⋊C8
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

1550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 167437);