Finite Group Databasebeta

C22×Dic124 #14521826

order1984
isoclinismisoclinic class of #92470
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic124

Splittings

SylowC31 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23D124
commutator, cosocleC4×C31C24
FrattiniC4C23×D31
FittingC22×C8×C31C2
socle, prime radicalC23×C31D4
hypercenterC22×C8D31
hypocenterC31C22×Q16
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

Relationships

maximal subgroup of#16846051, #16846053, #16846570, …
maximal normal subgroup of#16846051, #16846053, #16846570, …
maximal quotient ofC22×#11758404, C22×#11758406, C2×C4×Dic124, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 1326);