Finite Group Databasebeta

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C4×C52×C8×C9 #72186263

order7200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 368640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4×C5

Aliases

abelianC4×C52×C8×C9
multiplicative(ℤ/7421)ˣ, (ℤ/14842)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C4C22×C3×C52
socle, prime radicalC22×C3×C52C2×C3×C4
LCSG ▷ C1
UCSC1 ◁ G

528 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C52×C9×C16, C52×C82×C9, C2×C4×C52×C8×C9, …
maximal normal subgroup ofC4×C52×C9×C16, C52×C82×C9, C2×C4×C52×C8×C9, …
maximal quotient ofC4×C52×C9×C16, C52×C82×C9, C2×C4×C52×C8×C9, …
automorphism group ofC41×C181
outer automorphism group ofC41×C181

GAP

Past the SmallGroups library coverage — no SmallGroups id.