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Cayley diagram

C2×C52⋊C9 #90648

order450
isoclinismisoclinic class of C52⋊C3
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C5

Aliases

direct productC2×C52⋊C9
unambiguous semidirect product(C2×C52)⋊C9

Splittings

derived, SylowC52 ⋊ C2×C9
HallC2×C52 ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC2×C3C52⋊C3
commutator, hypocenterC52C2×C9
FrattiniC3C2×C52⋊C3
Fitting, socle, prime radicalC2×C3×C52C3
cosocleC3×C52C2×C3
LCSG ▷ C52
UCSC1 ◁ C2×C3

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 90

A minimal faithful permutation representation — 2 generators on 26 points:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

derived subgroup of#14267934, #14267936, #14267938, …
maximal subgroup of#11744607, #1039⋊C9, C4×C52⋊C9, …
maximal normal subgroup of#11744607, #1039⋊C9, C4×C52⋊C9, …
maximal quotient ofC4×C52⋊C9, C22×C52⋊C9, C2×C52⋊C27, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(450, 13);