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Q82×C283 #31826155

order18112
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C283 · Schur multiplier (H2) = C24

Aliases

direct productQ82×C283

Subgroups

subgroupG/H
center, socle, prime radicalC22×C283C24
commutator, Frattini, cosocleC22C24×C283
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C283 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18112

Conjugacy classes & character table

7075 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49120339, #49120401, #49120482, …
maximal subgroup of#1623×C283, #1633×C283, #1645×C283, …
maximal normal subgroup of#1623×C283, #1633×C283, #1645×C283, …
maximal quotient ofQ8×C4⋊C4×C283, #2369×C283, #2451×C283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18112, 239);