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Q82×C271 #31773587

order17344
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C271 · Schur multiplier (H2) = C24

Aliases

direct productQ82×C271

Subgroups

subgroupG/H
center, socle, prime radicalC22×C271C24
commutator, Frattini, cosocleC22C24×C271
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C271 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17344

Conjugacy classes & character table

6775 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46835442, #46835504, #46835585, …
maximal subgroup of#1623×C271, #1633×C271, #1645×C271, …
maximal normal subgroup of#1623×C271, #1633×C271, #1645×C271, …
maximal quotient ofQ8×C4⋊C4×C271, #2369×C271, #2451×C271, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17344, 239);