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C2×C11⋊C25 #10587747

order550
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C25 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11⋊C25
unambiguous semidirect product(C2×C11)⋊C25

Splittings

derived, SylowC11 ⋊ C2×C25
HallC2×C11 ⋊ C25

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊C5
commutator, hypocenterC11C2×C25
FrattiniC5C2×C11⋊C5
Fitting, socle, prime radicalC2×C5×C11C5
cosocleC5×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C5

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 550

A minimal faithful permutation representation — 2 generators on 38 points:

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic11⋊C25, C4×C11⋊C25, C2×D11⋊C25, …
maximal normal subgroup ofDic11⋊C25, C4×C11⋊C25, C2×D11⋊C25, …
maximal quotient ofC4×C11⋊C25, C22×C11⋊C25, D3×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(550, 2);