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Q82×C199 #27163708

order12736
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C199 · Schur multiplier (H2) = C24

Aliases

direct productQ82×C199

Subgroups

subgroupG/H
center, socle, prime radicalC22×C199C24
commutator, Frattini, cosocleC22C24×C199
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C199 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12736

Conjugacy classes & character table

4975 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#38767928, #38767990, #38768071, …
maximal subgroup of#1623×C199, #1633×C199, #1645×C199, …
maximal normal subgroup of#1623×C199, #1633×C199, #1645×C199, …
maximal quotient ofQ8×C4⋊C4×C199, #2369×C199, #2451×C199, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12736, 239);