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C11×Dic35 #13095355

order1540
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic35
unambiguous semidirect productC7⋊(C11×Dic5)

Splittings

derived, HallC5×C7 ⋊ C4×C11
HallC5×C7×C11 ⋊ C4
HallC7×C11 ⋊ Dic5
HallC5×C11 ⋊ Dic7
SylowC7 ⋊ C11×Dic5
SylowC5 ⋊ C11×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C11D35
commutator, hypocenterC5×C7C4×C11
FrattiniC2C11×D35
Fitting, socle, prime radicalC2×C5×C7×C11C2
cosocleC2×C5×C7C2×C11
LCSG ▷ C5×C7
UCSC1 ◁ C2×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 1540

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,18,19,20)(21,22,23,24,25,26,27);(12,14,13,15)(17,20)(18,19)(22,27)(23,26)(24,25)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C11×Dic35, C11×Dic105, C11×ΓL(1,𝔽8)⋊Dic5, …
maximal normal subgroup ofC3×C11×Dic35, C11×ΓL(1,𝔽8)⋊Dic5, C121×Dic35, …
maximal quotient ofC3×C11×Dic35, C11×Dic105, C11×C7⋊#4379, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1540, 10);