Finite Group Databasebeta

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C2×C3×D5×#6732 #72219145

order14400
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×D5×#6732

Splittings

derivedC5×SL(2,𝔽5) ⋊ C23×C3

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4D5×A5
commutator, hypocenterC5×SL(2,𝔽5)C23×C3
FrattiniC2C22×C3×D5×A5
FittingC2×C3×C4×C5C2×A5
socleC22×C3×C5C22×A5
cosocleC2×C5C23×C3×A5
LCSG ▷ C5×SL(2,𝔽5)
UCSC1 ◁ C2×C3×C4

2006 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 2006 conjugacy classes of subgroups — too many to draw. Only its 112 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

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.