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C22×C3×C5×C11×C23 #29503247

order15180
nilpotency class1
isoclinismisoclinic class of C1
automorphism?
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C3×C5×C11×C23
multiplicative(ℤ/15557)ˣ, (ℤ/15893)ˣ, (ℤ/16399)ˣ, (ℤ/16819)ˣ, (ℤ/17717)ˣ, (ℤ/22773)ˣ, (ℤ/22779)ˣ, (ℤ/30364)ˣ, (ℤ/31114)ˣ, (ℤ/31786)ˣ, (ℤ/32798)ˣ, (ℤ/33638)ˣ, (ℤ/35434)ˣ, (ℤ/45546)ˣ, (ℤ/45558)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 15180

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2)(5,6,7)(8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46);(3,4)

Conjugacy classes & character table

15180 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C5×C11×C23, C23×C3×C5×C11×C23
maximal normal subgroup ofC2×C3×C4×C5×C11×C23, C23×C3×C5×C11×C23
maximal quotient ofC2×C3×C4×C5×C11×C23, C23×C3×C5×C11×C23
automorphism group ofC47×C331, C23×C691, C7×C2531
outer automorphism group ofC47×C331, C23×C691, C7×C2531

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 33);