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C11⋊C5×Dic17 #16836656

order3740
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×Dic17
unambiguous semidirect product(C11×Dic17)⋊C5

Splittings

derived, HallC11×C17 ⋊ C4×C5
HallC17×C11⋊C5 ⋊ C4
HallC11×Dic17 ⋊ C5
SylowC17 ⋊ C4×C11⋊C5
SylowC11 ⋊ C5×Dic17

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D17×C11⋊C5
commutator, hypocenterC11×C17C4×C5
Fitting, socle, cosocleC2×C11×C17C2×C5
prime radicalC2×C17×C11⋊C5C2
LCSG ▷ C11×C17
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 748

A minimal faithful permutation representation — 2 generators on 32 points:

(2,3,5,8,7)(4,6,10,11,9)(12,13)(14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32);(1,2,4,7,3,5,9,11,6,8,10)(12,14,13,15)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊C5×Dic17, C11⋊C5×Dic51, C5×C11⋊C5×Dic17, …
maximal normal subgroup ofC3×C11⋊C5×Dic17, C5×C11⋊C5×Dic17, C7×C11⋊C5×Dic17
maximal quotient ofC3×C11⋊C5×Dic17, C11⋊C5×Dic51, Dic17×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 2);