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C7×C11⋊C25 #14515329

order1925
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11⋊C25
unambiguous semidirect productC11⋊(C7×C25)
unambiguous semidirect product(C7×C11)⋊C25

Splittings

derived, SylowC11 ⋊ C7×C25
HallC7×C11 ⋊ C25

Subgroups

subgroupG/H
center, hypercenterC5×C7C11⋊C5
commutator, hypocenterC11C7×C25
FrattiniC5C7×C11⋊C5
Fitting, socle, prime radicalC5×C7×C11C5
cosocleC5×C11C5×C7
LCSG ▷ C11
UCSC1 ◁ C5×C7

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 1925

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3,4,5,6,7)(9,10,12,15,14)(11,13,17,18,16)(19,20,22,25,29,21,23,26,30,34,24,27,31,35,38,28,32,36,39,41,33,37,40,42,43);(8,9,11,14,10,12,16,18,13,15,17)

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D11⋊C25, D7×C11⋊C25, C7⋊(D11⋊C25), …
maximal normal subgroup ofC7×D11⋊C25, D7×C11⋊C25, C7⋊(D11⋊C25), …
maximal quotient ofC2×C7×C11⋊C25, C49×C11⋊C25, C72×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1925, 1);