Finite Group Databasebeta

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C5×C11×Dic15 #15693141

order3300
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic15
unambiguous semidirect productC3⋊(C5×C11×Dic5)

Splittings

derivedC3×C5 ⋊ C4×C5×C11
HallC3×C52×C11 ⋊ C4
HallC52×C11 ⋊ Dic3
HallC3×C52 ⋊ C4×C11
HallC3×C11 ⋊ C5×Dic5
SylowC52 ⋊ C11×Dic3
SylowC3 ⋊ C5×C11×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D15
commutator, hypocenterC3×C5C4×C5×C11
FrattiniC2C5×C11×D15
Fitting, socle, prime radicalC2×C3×C52×C11C2
cosocleC2×C3×C5C2×C5×C11
LCSG ▷ C3×C5
UCSC1 ◁ C2×C5×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C11×Dic105, C5×C7×C11×Dic15, C5×Dic15×C121, …
maximal normal subgroup ofC5×C7×C11×Dic15, C5×Dic15×C121, C5×C112×Dic15
maximal quotient ofC5×C11×Dic105, C5×C7×C11×Dic15, C5×Dic15×C121, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 61);