Finite Group Databasebeta

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C2×C4×C7×C107 #72185185

order5992
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5088
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C7×C107
multiplicative(ℤ/7495)ˣ, (ℤ/14990)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C7×C107
socle, prime radicalC22×C7×C107C2
LCSG ▷ C1
UCSC1 ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5992 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C8×C107, C42×C7×C107, C22×C4×C7×C107, …
maximal normal subgroup ofC2×C7×C8×C107, C42×C7×C107, C22×C4×C7×C107, …
maximal quotient ofC2×C7×C8×C107, C42×C7×C107, C22×C4×C7×C107, …
automorphism group ofC5×C1499
outer automorphism group ofC5×C1499

GAP

Past the SmallGroups library coverage — no SmallGroups id.