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C4×C5×C7×C16 #72182184

order2240
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6144
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C5×C7×C16
multiplicative(ℤ/2825)ˣ, (ℤ/5650)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C22×C5×C7
socle, prime radicalC22×C5×C7C2×C8
LCSG ▷ C1
UCSC1 ◁ G

116 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C7×C32, C5×C7×C8×C16, C2×C4×C5×C7×C16, …
maximal normal subgroup ofC4×C5×C7×C32, C5×C7×C8×C16, C2×C4×C5×C7×C16, …
maximal quotient ofC4×C5×C7×C32, C5×C7×C8×C16, C2×C4×C5×C7×C16, …
automorphism group ofC25×C113, C2×C25×C113
outer automorphism group ofC25×C113, C2×C25×C113

GAP

Past the SmallGroups library coverage — no SmallGroups id.