Finite Group Databasebeta

C2×(C2×D83)⋊#95 #35325492

order21248
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C210

Aliases

direct productC2×(C2×D83)⋊#95

Splittings

FittingC22×#95×C83 ⋊ C2
SylowC83 ⋊ C2×C22⋊#95

Subgroups

subgroupG/H
centerC25C22×D83
commutatorC22×C83C22×C42
FrattiniC24C23×D83
FittingC22×#95×C83C2
socleC25×C83C23
prime radicalC25×D83C22
cosocleC24×C83C24
hypercenterC22×#95D83
hypocenterC83C2×C22⋊#95
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C25 ◁ C22×#95

7630 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, 90656);