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#585×C97 #20260452

order6208
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C25×C97 · Schur multiplier (H2) = C29

Aliases

direct product#585×C97

Subgroups

subgroupG/H
centerC4×C97C24
commutator, Frattini, cosocleC2C25×C97
socleC2×C97C25
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C4×C97 ◁ G

810 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3298 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC97×#1791, C97×#1794, C97×#2901, …
maximal normal subgroup ofC97×#1791, C97×#1794, C97×#2901, …
maximal quotient ofC97×#3428, C4×H(5,𝔽2)×C97, C4×2−1+4×C97, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 266);