Finite Group Databasebeta

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SD16×#64424 #72245136

order4704
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productSD16×#64424

Splittings

FittingC72×SD16 ⋊ C2×C3
HallSD16×C7⋊D7 ⋊ C3
Hall#3861 ⋊ C2×SD16
SylowC72 ⋊ C2×C3×SD16

Subgroups

subgroupG/H
centerC2D4×#64424
commutator, cosocleC4×C72C23×C3
FrattiniC4C22×#64424
FittingC72×SD16C2×C3
socleC2×C72C2×C3×D4
prime radicalD4×#64424C2
hypercenterSD16#64424
hypocenterC72C2×C3×SD16
LCSG ▷ C4×C72 ▷ C2×C72 ▷ C72
UCSC1 ◁ C2 ◁ C4 ◁ SD16

680 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 392

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/8)×#64424, SD16×ΓL(1,𝔽8)⋊AGL(1,𝔽7), C2×SD16×#64424
maximal normal subgroup ofAGL(1,ℤ/8)×#64424, SD16×ΓL(1,𝔽8)⋊AGL(1,𝔽7), C2×SD16×#64424
maximal quotient ofC2×SD16×#64424, #106×#64424, #102×#64424

GAP

Past the SmallGroups library coverage — no SmallGroups id.