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C22×C3×C52×C49 #28412924

order14700
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 241920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C5

Aliases

abelianC22×C3×C52×C49
multiplicative(ℤ/15221)ˣ, (ℤ/16181)ˣ, (ℤ/30442)ˣ, (ℤ/32362)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC7C22×C3×C52×C7
socle, prime radicalC22×C3×C52×C7C7
LCSG ▷ C1
UCSC1 ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14700 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C52×C49, C23×C3×C52×C49
maximal normal subgroup ofC2×C3×C4×C52×C49, C23×C3×C52×C49
maximal quotient ofC2×C3×C4×C52×C49, C23×C3×C52×C49
automorphism group ofC31×C491, C11×C1471
outer automorphism group ofC31×C491, C11×C1471

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 103);