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Q82×C197 #27160769

order12608
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C197 · Schur multiplier (H2) = C24

Aliases

direct productQ82×C197

Subgroups

subgroupG/H
center, socle, prime radicalC22×C197C24
commutator, Frattini, cosocleC22C24×C197
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C197 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12608

Conjugacy classes & character table

4925 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#38741790, #38741852, #38741933, …
maximal subgroup of#1623×C197, #1633×C197, #1645×C197, …
maximal normal subgroup of#1623×C197, #1633×C197, #1645×C197, …
maximal quotient ofQ8×C4⋊C4×C197, #2369×C197, #2451×C197, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12608, 239);