Finite Group Databasebeta

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C3×#13104792 #72230909

order4800
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×#13104792

Splittings

FittingC2×C3×C52×D4 ⋊ C4
HallC3×C52 ⋊ #390
SylowC52 ⋊ C3×#390

Subgroups

subgroupG/H
centerC22×C3C22×#1043
commutatorC22×C52C22×C3×C4
FrattiniC22C22×C3×#1043
FittingC2×C3×C52×D4C4
socleC22×C3×C52C22×C4
prime radicalC2×C3×D4×C5⋊D5C2
cosocleC22×C5⋊D5C23×C3
hypercenterC2×C3×D4#1043
hypocenterC52C3×#390
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

2064 conjugacy classes of subgroups; only the 260 normal subgroups are shown.

normal subgroups only

This group has 2064 conjugacy classes of subgroups — too many to draw. Only its 260 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) = 1200

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×#127×#1043, D3×#13104792, #72231313
maximal normal subgroup ofC3×#127×#1043, D3×#13104792, #72231313

GAP

Past the SmallGroups library coverage — no SmallGroups id.