Finite Group Databasebeta

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C2×C3×C5×GL(2,𝔽5) #72219125

order14400
isoclinismisoclinic class of #6728
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×GL(2,𝔽5)

Splittings

derivedSL(2,𝔽5) ⋊ C2×C3×C4×C5

Subgroups

subgroupG/H
center, Fitting, hypercenterC2×C3×C4×C5S5
commutator, hypocenterSL(2,𝔽5)C2×C3×C4×C5
FrattiniC4C2×C3×C5×S5
socleC22×C3×C5A5⋊C4
prime radicalC2×C3×C5×#6732C2
cosocle#6732C22×C3×C5
LCSG ▷ SL(2,𝔽5)
UCSC1 ◁ C2×C3×C4×C5

712 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 64 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

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.