Finite Group Databasebeta

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C2×C5×C8×C173 #72192076

order13840
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 11008
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C5×C8×C173
multiplicative(ℤ/14227)ˣ, (ℤ/28454)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C5×C173
socle, prime radicalC22×C5×C173C4
LCSG ▷ C1
UCSC1 ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C16×C173, C4×C5×C8×C173, C22×C5×C8×C173
maximal normal subgroup ofC2×C5×C16×C173, C4×C5×C8×C173, C22×C5×C8×C173
maximal quotient ofC2×C5×C16×C173, C4×C5×C8×C173, C22×C5×C8×C173
automorphism group ofC41×C347
outer automorphism group ofC41×C347

GAP

Past the SmallGroups library coverage — no SmallGroups id.