Finite Group Databasebeta

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3−1+2×#6038 #72254647

order5400
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2

Aliases

direct product3−1+2×#6038

Splittings

HallC52×3−1+2 ⋊ D4
SylowC52 ⋊ D4×3−1+2

Subgroups

subgroupG/H
center, FrattiniC2×C3C32×D52
commutator, socle, cosocleC2×C3×C52C22×C32
FittingC2×C52×3−1+2C22
prime radicalC32×#6038C3
hypercenterC2×3−1+2D52
hypocenterC52D4×3−1+2
LCSG ▷ C2×C3×C52 ▷ C52
UCSC1 ◁ C2×C3 ◁ C2×3−1+2

336 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 180

Conjugacy classes & character table

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

Relationships

maximal subgroup of3−1+2×#87886, AGL(1,ℤ/9)×#6038, #72254771
maximal normal subgroup of3−1+2×#87886, AGL(1,ℤ/9)×#6038, #72254771

GAP

Past the SmallGroups library coverage — no SmallGroups id.