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C2×C3×C4×C5⋊D5 #11925686

order1200
isoclinismisoclinic class of C5⋊D5
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C5

Aliases

direct productC2×C3×C4×C5⋊D5

Splittings

FittingC2×C3×C4×C52 ⋊ C2
derived, SylowC52 ⋊ C22×C3×C4
HallC3×C52 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4C5⋊D5
commutator, hypocenterC52C22×C3×C4
FrattiniC2C22×C3×C5⋊D5
FittingC2×C3×C4×C52C2
socleC22×C3×C52C22
prime radicalC22×C3×C5⋊D5C2
cosocleC2×C52C23×C3
LCSG ▷ C52
UCSC1 ◁ C2×C3×C4

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 600

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3×C4×#1044, C2×C3×C4×D52, C2×C3×C4×#1043, …
maximal normal subgroup ofC2×C3×C4×#1044, C2×C3×C4×D52, C2×C3×C4×#1043, …
maximal quotient ofC2×C3×C4×#6953, C3×C42×C5⋊D5, C2×C3×Dic3×C5⋊D5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 896);