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Q82×C239 #29504462

order15296
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C239 · Schur multiplier (H2) = C24

Aliases

direct productQ82×C239

Subgroups

subgroupG/H
center, socle, prime radicalC22×C239C24
commutator, Frattini, cosocleC22C24×C239
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C239 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15296

Conjugacy classes & character table

5975 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44483626, #44483688, #44483769, …
maximal subgroup of#1623×C239, #1633×C239, #1645×C239, …
maximal normal subgroup of#1623×C239, #1633×C239, #1645×C239, …
maximal quotient ofQ8×C4⋊C4×C239, #2369×C239, #2451×C239, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15296, 239);