Finite Group Databasebeta

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C3×C11×Dic85 #26014331

order11220
isoclinismisoclinic class of D85
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×Dic85

Splittings

derived, HallC5×C17 ⋊ C3×C4×C11
HallC3×C5×C11×C17 ⋊ C4
HallC5×C11×C17 ⋊ C3×C4
HallC3×C11×C17 ⋊ Dic5
HallC3×C5×C17 ⋊ C4×C11
HallC11×C17 ⋊ C3×Dic5
HallC3×C5×C11 ⋊ Dic17
HallC5×C11 ⋊ C3×Dic17
HallC3×C17 ⋊ C11×Dic5
SylowC17 ⋊ C3×C11×Dic5
HallC3×C5 ⋊ C11×Dic17
SylowC5 ⋊ C3×C11×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D85
commutator, hypocenterC5×C17C3×C4×C11
FrattiniC2C3×C11×D85
Fitting, socle, prime radicalC2×C3×C5×C11×C17C2
cosocleC2×C5×C17C2×C3×C11
LCSG ▷ C5×C17
UCSC1 ◁ C2×C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2904 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C11×Dic85, C3×C11×Dic255, C32×C11×Dic85
maximal normal subgroup ofC9×C11×Dic85, C32×C11×Dic85
maximal quotient ofC9×C11×Dic85, C3×C11×Dic255, C32×C11×Dic85

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 7);