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C4×C29×C107 #27137209

order12412
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5936
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC12412
abelianC4×C29×C107
multiplicative(ℤ/12413)ˣ, (ℤ/24826)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C29×C107
socle, prime radicalC2×C29×C107C2
LCSG ▷ C1
UCSC1 ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12412 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic12412, D24824
maximal subgroup ofC3×C4×C29×C107, Dic3×C29×C107, C8×C29×C107, …
maximal normal subgroup ofC3×C4×C29×C107, C8×C29×C107, C2×C4×C29×C107, …
maximal quotient ofC3×C4×C29×C107, Dic3×C29×C107, C8×C29×C107, …
automorphism group ofC12413
outer automorphism group ofC12413

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12412, 1);