Finite Group Databasebeta

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C2×C3×#72213713 #72217933

order25920
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×#72213713

Splittings

Fitting, socleC2×C33×C5 ⋊ #859
derivedC5×PSU(3,𝔽2)⋊C3 ⋊ C2×C3×C4
SylowC5 ⋊ C2×C3×(PSU(3,𝔽2)⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3#72213713
commutator, hypocenterC5×PSU(3,𝔽2)⋊C3C2×C3×C4
FrattiniC1G
Fitting, socleC2×C33×C5#859
prime radicalC2×C3×D5×PSU(3,𝔽2)⋊C3C2
cosocleD5×PSU(3,𝔽2)⋊C3C22×C3
LCSG ▷ C5×PSU(3,𝔽2)⋊C3
UCSC1 ◁ C2×C3

1298 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 1298 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×AGL(1,𝔽5)×AGL(2,𝔽3)
maximal normal subgroup ofC2×C3×AGL(1,𝔽5)×AGL(2,𝔽3)

GAP

Past the SmallGroups library coverage — no SmallGroups id.