Finite Group Databasebeta

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C4×C5×C8×C73 #72190145

order11680
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 36864
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C5×C8×C73
multiplicative(ℤ/12013)ˣ, (ℤ/24026)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C22×C5×C73
socle, prime radicalC22×C5×C73C2×C4
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C16×C73, C5×C82×C73, C2×C4×C5×C8×C73
maximal normal subgroup ofC4×C5×C16×C73, C5×C82×C73, C2×C4×C5×C8×C73
maximal quotient ofC4×C5×C16×C73, C5×C82×C73, C2×C4×C5×C8×C73
automorphism group ofC41×C293
outer automorphism group ofC41×C293

GAP

Past the SmallGroups library coverage — no SmallGroups id.