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C3×C5×Dic55 #15693136

order3300
isoclinismisoclinic class of D55
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic55

Splittings

derivedC5×C11 ⋊ C3×C4×C5
HallC3×C52×C11 ⋊ C4
HallC52×C11 ⋊ C3×C4
HallC3×C52 ⋊ Dic11
HallC3×C11 ⋊ C5×Dic5
SylowC52 ⋊ C3×Dic11
SylowC11 ⋊ C3×C5×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D55
commutator, hypocenterC5×C11C3×C4×C5
FrattiniC2C3×C5×D55
Fitting, socle, prime radicalC2×C3×C52×C11C2
cosocleC2×C5×C11C2×C3×C5
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C11⋊(ΓL(1,𝔽8)⋊Dic5), C5×ΓL(1,𝔽8)×Dic55, C3×C5×Dic385, …
maximal normal subgroup ofC3×C5×C7×Dic55, C3×C5×C11×Dic55
maximal quotient ofC5×C11⋊(ΓL(1,𝔽8)⋊Dic5), C5×ΓL(1,𝔽8)×Dic55, C3×C5×Dic385, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 56);